import java.io.InputStream;
import java.util.Arrays;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class Main {
public static void main(String[] args) throws Exception {
ExtendedScanner sc = new ExtendedScanner();
FastPrintStream pw = new FastPrintStream();
solve(sc, pw);
sc.close();
pw.flush();
pw.close();
}
public static void solve(ExtendedScanner sc, FastPrintStream pw) {
int n = sc.nextInt();
int m = sc.nextInt();
DisjointSetUnion dsu = new DisjointSetUnion(n);
ForestBuilder fb = new ForestBuilder(2 * n - 1);
int[] root = new int[n];
Arrays.setAll(root, i -> i);
int[] time = new int[2 * n - 1];
for (int i = 0, idx = n; i < m; i++) {
int x = sc.nextInt() - 1;
int y = sc.nextInt() - 1;
if (dsu.same(x, y)) continue;
x = dsu.leader(x);
y = dsu.leader(y);
fb.addEdge(root[x], idx);
fb.addEdge(root[y], idx);
root[dsu.merge(x, y)] = idx;
time[idx] = i + 1;
idx++;
}
Forest f = fb.build();
int groupNum = f.groupNum();
Tree[] ts = f.toTrees();
EulerTourLCA[] lcas = new EulerTourLCA[groupNum];
for (int i = 0; i < groupNum; i++) {
lcas[i] = new EulerTourLCA(ts[i]);
}
int q = sc.nextInt();
while (q --> 0) {
int x = sc.nextInt() - 1;
int y = sc.nextInt() - 1;
int idx = f.id(x);
int idy = f.id(y);
if (idx != idy) {
pw.println(-1);
continue;
}
int ix = f.inv(x);
int iy = f.inv(y);
int ia = lcas[idx].query(ix, iy);
int a = f.group(idx)[ia];
pw.println(time[a]);
}
}
}
final class DisjointSetUnion {
final int N;
final int[] Dat;
public DisjointSetUnion(int n) {
this.N = n;
this.Dat = new int[N];
clear();
}
public int merge(int x, int y) {
x = leader(x);
y = leader(y);
if (x == y) return x;
if (-Dat[y] > -Dat[x]) {
int tmp = x; x = y; y = tmp;
}
Dat[x] += Dat[y];
Dat[y] = x;
return x;
}
public boolean same(int x, int y) {
return leader(x) == leader(y);
}
public int leader(int x) {
if (x < 0 || x >= N) {
throw new IndexOutOfBoundsException(
String.format("Index %d out of bounds for the length %d.", x, N)
);
}
if (Dat[x] < 0) return x;
return Dat[x] = leader(Dat[x]);
}
public int size(int x) {
return -Dat[leader(x)];
}
public int[][] groups() {
int[] cmp = new int[N];
int[] cnt = new int[N];
int groupNum = 0;
for (int i = 0; i < N; i++) {
if (Dat[i] < 0) {
cnt[cmp[i] = groupNum++] = -Dat[i];
}
}
int[][] groups = new int[groupNum][];
for (int j = 0; j < groupNum; j++) {
groups[j] = new int[cnt[j]];
}
for (int i = 0; i < N; i++) {
int j = cmp[leader(i)];
groups[j][--cnt[j]] = i;
}
return groups;
}
public void clear() {
java.util.Arrays.fill(Dat, -1);
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
final class ExtendedScanner extends FastScanner {
public ExtendedScanner() {super();}
public ExtendedScanner(InputStream in) {super(in);}
public int[] ints(final int n) {
final int[] a = new int[n];
Arrays.setAll(a, $ -> nextInt());
return a;
}
public int[] ints(final int n, final IntUnaryOperator f) {
final int[] a = new int[n];
Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
return a;
}
public int[][] ints(final int n, final int m) {
final int[][] a = new int[n][];
Arrays.setAll(a, $ -> ints(m));
return a;
}
public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
final int[][] a = new int[n][];
Arrays.setAll(a, $ -> ints(m, f));
return a;
}
public long[] longs(final int n) {
final long[] a = new long[n];
Arrays.setAll(a, $ -> nextLong());
return a;
}
public long[] longs(final int n, final LongUnaryOperator f) {
final long[] a = new long[n];
Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
return a;
}
public long[][] longs(final int n, final int m) {
final long[][] a = new long[n][];
Arrays.setAll(a, $ -> longs(m));
return a;
}
public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
final long[][] a = new long[n][];
Arrays.setAll(a, $ -> longs(m, f));
return a;
}
public char[][] charArrays(final int n) {
final char[][] c = new char[n][];
Arrays.setAll(c, $ -> nextChars());
return c;
}
public double[] doubles(final int n) {
final double[] a = new double[n];
Arrays.setAll(a, $ -> nextDouble());
return a;
}
public double[][] doubles(final int n, final int m) {
final double[][] a = new double[n][];
Arrays.setAll(a, $ -> doubles(m));
return a;
}
public String[] strings(final int n) {
final String[] s = new String[n];
Arrays.setAll(s, $ -> next());
return s;
}
}
class Forest {
final int n;
final int groupNum;
final int[][] adj;
final int[] ids;
final int[] inv;
final int[] par;
final int[][] groups;
final int[] roots;
final int[][] pre;
final int[][] pst;
Forest(int n, int[][] adj, int[][] groups, int[] ids, int[] inv, int[] root) {
this.n = n;
this.groupNum = groups.length;
this.adj = adj;
this.ids = ids;
this.inv = inv;
this.par = new int[n];
this.groups = groups;
this.roots = new int[groupNum];
this.pre = new int[groupNum][];
this.pst = new int[groupNum][];
build(root);
}
private void build(int[] root) {
int[] stack = new int[n << 1];
java.util.Arrays.fill(par, -1);
for (int i = 0; i < groupNum; i++) {
int siz_i = groups[i].length;
int fst = groups[i][0], r = root[fst];
int root_i = roots[i] = r < 0 ? fst : r;
int[] pre_i = pre[i] = new int[siz_i];
int[] pst_i = pst[i] = new int[siz_i];
int preOrd = 0, pstOrd = 0;
int ptr = 0;
stack[ptr++] = ~root_i;
stack[ptr++] = root_i;
while (ptr > 0) {
int u = stack[--ptr];
if (u >= 0) {
pre_i[preOrd++] = u;
for (int v : adj[u]) {
if (v == par[u]) continue;
par[v] = u;
stack[ptr++] = ~v;
stack[ptr++] = v;
}
} else {
pst_i[pstOrd++] = ~u;
}
}
}
}
public final int getV() {
return n;
}
public final int groupNum() {
return groupNum;
}
public final int[] edges(int u) {
return adj[u];
}
public final int parent(int u) {
return par[u];
}
public final int[] parent() {
return par;
}
public final int[] ids() {
return ids;
}
public final int[] invs() {
return inv;
}
public final int id(int u) {
return ids[u];
}
public final int inv(int u) {
return inv[u];
}
public final int[] group(int id) {
return groups[id];
}
public final int root(int id) {
return roots[id];
}
public final int size(int id) {
return groups[id].length;
}
public final int[] preOrder(int id) {
return pre[id];
}
public final int[] postOrder(int id) {
return pst[id];
}
public final Tree[] toTrees() {
Tree[] ts = new Tree[groupNum];
for (int id = 0; id < groupNum; id++) {
int size = size(id);
TreeBuilder tb = new TreeBuilder(size);
for (int u : group(id)) {
int v = par[u];
if (v < 0) continue;
tb.addEdge(inv[u], inv[v]);
}
ts[id] = tb.build();
}
return ts;
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class FastPrintStream implements AutoCloseable {
private static final int INT_MAX_LEN = 11;
private static final int LONG_MAX_LEN = 20;
private int precision = 9;
private static final int BUF_SIZE = 1 << 14;
private static final int BUF_SIZE_MINUS_INT_MAX_LEN = BUF_SIZE - INT_MAX_LEN;
private static final int BUF_SIZE_MINUS_LONG_MAX_LEN = BUF_SIZE - LONG_MAX_LEN;
private final byte[] buf = new byte[BUF_SIZE];
private int ptr = 0;
private final java.lang.reflect.Field strField;
private final java.nio.charset.CharsetEncoder encoder;
private final java.io.OutputStream out;
public FastPrintStream(java.io.OutputStream out) {
this.out = out;
java.lang.reflect.Field f;
try {
f = java.lang.String.class.getDeclaredField("value");
f.setAccessible(true);
} catch (NoSuchFieldException | SecurityException e) {
f = null;
}
this.strField = f;
this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
}
public FastPrintStream(java.io.File file) throws java.io.IOException {
this(new java.io.FileOutputStream(file));
}
public FastPrintStream(java.lang.String filename) throws java.io.IOException {
this(new java.io.File(filename));
}
public FastPrintStream() {
this(new java.io.FileOutputStream(java.io.FileDescriptor.out));
}
public FastPrintStream println() {
if (ptr == BUF_SIZE) internalFlush();
buf[ptr++] = (byte) '\n';
return this;
}
public FastPrintStream println(java.lang.Object o) {
return print(o).println();
}
public FastPrintStream println(java.lang.String s) {
return print(s).println();
}
public FastPrintStream println(char[] s) {
return print(s).println();
}
public FastPrintStream println(char c) {
return print(c).println();
}
public FastPrintStream println(int x) {
return print(x).println();
}
public FastPrintStream println(long x) {
return print(x).println();
}
public FastPrintStream println(double d, int precision) {
return print(d, precision).println();
}
public FastPrintStream println(double d) {
return print(d).println();
}
private FastPrintStream print(byte[] bytes) {
int n = bytes.length;
if (ptr + n > BUF_SIZE) {
internalFlush();
try {
out.write(bytes);
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
} else {
System.arraycopy(bytes, 0, buf, ptr, n);
ptr += n;
}
return this;
}
public FastPrintStream print(java.lang.Object o) {
return print(o.toString());
}
public FastPrintStream print(java.lang.String s) {
if (strField == null) {
return print(s.getBytes());
} else {
try {
Object value = strField.get(s);
if (value instanceof byte[]) {
return print((byte[]) value);
} else {
return print((char[]) value);
}
} catch (IllegalAccessException e) {
return print(s.getBytes());
}
}
}
public FastPrintStream print(char[] s) {
try {
return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
} catch (java.nio.charset.CharacterCodingException e) {
byte[] bytes = new byte[s.length];
for (int i = 0; i < s.length; i++) {
bytes[i] = (byte) s[i];
}
return print(bytes);
}
}
public FastPrintStream print(char c) {
if (ptr == BUF_SIZE) internalFlush();
buf[ptr++] = (byte) c;
return this;
}
public FastPrintStream print(int x) {
if (ptr > BUF_SIZE_MINUS_INT_MAX_LEN) internalFlush();
if (-10 < x && x < 10) {
if (x < 0) {
buf[ptr++] = '-';
x = -x;
}
buf[ptr++] = (byte) ('0' + x);
return this;
}
int d;
if (x < 0) {
if (x == Integer.MIN_VALUE) {
buf[ptr++] = '-'; buf[ptr++] = '2'; buf[ptr++] = '1'; buf[ptr++] = '4';
buf[ptr++] = '7'; buf[ptr++] = '4'; buf[ptr++] = '8'; buf[ptr++] = '3';
buf[ptr++] = '6'; buf[ptr++] = '4'; buf[ptr++] = '8';
return this;
}
d = len(x = -x);
buf[ptr++] = '-';
} else {
d = len(x);
}
int j = ptr += d;
while (x > 0) {
buf[--j] = (byte) ('0' + (x % 10));
x /= 10;
}
return this;
}
public FastPrintStream print(long x) {
if ((int) x == x) return print((int) x);
if (ptr > BUF_SIZE_MINUS_LONG_MAX_LEN) internalFlush();
int d;
if (x < 0) {
if (x == Long.MIN_VALUE) {
buf[ptr++] = '-'; buf[ptr++] = '9'; buf[ptr++] = '2'; buf[ptr++] = '2';
buf[ptr++] = '3'; buf[ptr++] = '3'; buf[ptr++] = '7'; buf[ptr++] = '2';
buf[ptr++] = '0'; buf[ptr++] = '3'; buf[ptr++] = '6'; buf[ptr++] = '8';
buf[ptr++] = '5'; buf[ptr++] = '4'; buf[ptr++] = '7'; buf[ptr++] = '7';
buf[ptr++] = '5'; buf[ptr++] = '8'; buf[ptr++] = '0'; buf[ptr++] = '8';
return this;
}
d = len(x = -x);
buf[ptr++] = '-';
} else {
d = len(x);
}
int j = ptr += d;
while (x > 0) {
buf[--j] = (byte) ('0' + (x % 10));
x /= 10;
}
return this;
}
public FastPrintStream print(double d, int precision) {
if (d < 0) {
print('-');
d = -d;
}
d += Math.pow(10, -precision) / 2;
print((long) d).print('.');
d -= (long) d;
for(int i = 0; i < precision; i++){
d *= 10;
print((int) d);
d -= (int) d;
}
return this;
}
public FastPrintStream print(double d) {
return print(d, precision);
}
public void setPrecision(int precision) {
this.precision = precision;
}
private void internalFlush() {
try {
out.write(buf, 0, ptr);
ptr = 0;
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
public void flush() {
try {
out.write(buf, 0, ptr);
out.flush();
ptr = 0;
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
public void close() {
try {
out.close();
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
private static int len(int x) {
return
x >= 1000000000 ? 10 :
x >= 100000000 ? 9 :
x >= 10000000 ? 8 :
x >= 1000000 ? 7 :
x >= 100000 ? 6 :
x >= 10000 ? 5 :
x >= 1000 ? 4 :
x >= 100 ? 3 :
x >= 10 ? 2 : 1;
}
private static int len(long x) {
return
x >= 1000000000000000000l ? 19 :
x >= 100000000000000000l ? 18 :
x >= 10000000000000000l ? 17 :
x >= 1000000000000000l ? 16 :
x >= 100000000000000l ? 15 :
x >= 10000000000000l ? 14 :
x >= 1000000000000l ? 13 :
x >= 100000000000l ? 12 :
x >= 10000000000l ? 11 : 10;
}
}
final class ForestBuilder {
private final int[] dsu;
private int t = 0;
private final int[] time;
private final int[] root;
private final int n;
private int ptr = 0;
private final SimpleEdge[] edges;
private final int[] count;
public ForestBuilder(int n) {
this.n = n;
this.dsu = new int[n];
java.util.Arrays.fill(dsu, -1);
this.time = new int[n];
this.root = new int[n];
java.util.Arrays.fill(root, -1);
this.edges = new SimpleEdge[n - 1];
this.count = new int[n];
}
public void setRoot(int u) {
root[leader(u)] = u;
time[u] = ++t;
}
public void setRootIfAbsent(int u) {
if (root[leader(u)] < 0) {
root[leader(u)] = u;
time[u] = ++t;
}
}
public boolean isConnected(int u, int v) {
return leader(u) == leader(v);
}
public int addEdgeIfDisconnected(int u, int v, long cost) {
if (leader(u) != leader(v)) return addEdge(u, v);
return -1;
}
public int addEdgeIfDisconnected(int u, int v) {
return addEdgeIfDisconnected(u, v, 1);
}
public int addEdge(int u, int v, long cost) {
if (leader(u) == leader(v)) throw new AssertionError();
edges[ptr] = new SimpleEdge(u, v, cost);
count[u]++;
count[v]++;
merge(u, v);
return ptr++;
}
public int addEdge(int u, int v) {
return addEdge(u, v, 1);
}
public Forest build() {
int[][] adj = new int[n][];
for (int i = 0; i < n; i++) adj[i] = new int[count[i]];
for (int i = 0; i < ptr; i++) {
int u = edges[i].from;
int v = edges[i].to;
adj[u][--count[u]] = v;
adj[v][--count[v]] = u;
}
for (int i = 0; i < n; i++) root[i] = root[leader(i)];
int[] inv = new int[n];
int[] ids = new int[n];
int[][] groups = groups(inv, ids);
return new Forest(n, adj, groups, ids, inv, root);
}
public WeightedForest buildWeightedForest() {
int[][] adj = new int[n][];
long[][] cst = new long[n][];
for (int i = 0; i < n; i++) {
adj[i] = new int[count[i]];
cst[i] = new long[count[i]];
}
for (int i = 0; i < ptr; i++) {
int u = edges[i].from;
int v = edges[i].to;
adj[u][--count[u]] = v;
adj[v][--count[v]] = u;
cst[u][count[u]] = edges[i].cost;
cst[v][count[v]] = edges[i].cost;
}
int[] inv = new int[n];
int[] ids = new int[n];
int[][] groups = groups(inv, ids);
return new WeightedForest(n, adj, groups, ids, inv, root, cst);
}
private int merge(int x, int y) {
x = leader(x);
y = leader(y);
if (x == y) return x;
if (-dsu[y] > -dsu[x]) {
int tmp = x; x = y; y = tmp;
}
dsu[x] += dsu[y];
dsu[y] = x;
int rx = root[x], ry = root[y];
if (ry >= 0 && (rx < 0 || time[rx] < time[ry])) {
root[x] = ry;
}
return x;
}
private int leader(int x) {
int p = dsu[x];
return p < 0 ? x : (dsu[x] = leader(p));
}
private int[][] groups(int[] inv, int[] ids) {
int[] cnt = new int[n];
int groupNum = 0;
for (int i = 0; i < n; i++) {
if (dsu[i] < 0) cnt[ids[i] = groupNum++] = -dsu[i];
}
int[][] groups = new int[groupNum][];
for (int j = 0; j < groupNum; j++) {
groups[j] = new int[cnt[j]];
}
for (int i = 0; i < n; i++) {
int j = ids[leader(i)];
groups[ids[i] = j][inv[i] = --cnt[j]] = i;
}
return groups;
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class Tree {
final int n;
final int root;
final int[][] adj;
final int[] par;
final int[] pre;
final int[] pst;
Tree(int n, int root, int[][] adj) {
this.n = n;
this.adj = adj;
this.root = root;
this.par = new int[n];
this.pre = new int[n];
this.pst = new int[n];
build();
}
private void build() {
int preOrd = 0, pstOrd = 0;
java.util.Arrays.fill(par, -1);
int[] stack = new int[n << 1];
int ptr = 0;
stack[ptr++] = ~root;
stack[ptr++] = root;
while (ptr > 0) {
int u = stack[--ptr];
if (u >= 0) {
pre[preOrd++] = u;
for (int v : adj[u]) {
if (v == par[u]) continue;
par[v] = u;
stack[ptr++] = ~v;
stack[ptr++] = v;
}
} else {
pst[pstOrd++] = ~u;
}
}
}
public int getV() {
return n;
}
public int getRoot() {
return root;
}
public int[] getEdges(int u) {
return adj[u];
}
public int[] parent() {
return par;
}
public int[] preOrder() {
return pre;
}
public int[] postOrder() {
return pst;
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class WeightedTree extends Tree {
final long[] cst;
final long[][] adjCost;
WeightedTree(int n, int root, int[][] adj, long[][] adjCost) {
super(n, root, adj);
this.cst = new long[n];
this.adjCost = adjCost;
for (int u = 0; u < n; u++) {
int k = adj[u].length;
for (int i = 0; i < k; i++) {
int v = adj[u][i];
long c = adjCost[u][i];
if (v == par[u]) {
cst[u] = c;
} else {
cst[v] = c;
}
}
}
}
public long[] getWeights() {
return cst;
}
public long getWeight(int u, int i) {
return adjCost[u][i];
}
}
/**
* @author https://atcoder.jp/users/suisen
*/
class FastScanner implements AutoCloseable {
private final ByteBuffer tokenBuf = new ByteBuffer();
private final java.io.InputStream in;
private final byte[] rawBuf = new byte[1 << 14];
private int ptr = 0;
private int buflen = 0;
public FastScanner(java.io.InputStream in) {
this.in = in;
}
public FastScanner() {
this(new java.io.FileInputStream(java.io.FileDescriptor.in));
}
private final int readByte() {
if (ptr < buflen) return rawBuf[ptr++];
ptr = 0;
try {
buflen = in.read(rawBuf);
if (buflen > 0) {
return rawBuf[ptr++];
} else {
throw new java.io.EOFException();
}
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
private final int readByteUnsafe() {
if (ptr < buflen) return rawBuf[ptr++];
ptr = 0;
try {
buflen = in.read(rawBuf);
if (buflen > 0) {
return rawBuf[ptr++];
} else {
return -1;
}
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
private final int skipUnprintableChars() {
int b = readByte();
while (b <= 32 || b >= 127) b = readByte();
return b;
}
private final void loadToken() {
tokenBuf.clear();
for (int b = skipUnprintableChars(); 32 < b && b < 127; b = readByteUnsafe()) {
tokenBuf.append(b);
}
}
public final boolean hasNext() {
for (int b = readByteUnsafe(); b <= 32 || b >= 127; b = readByteUnsafe()) {
if (b == -1) return false;
}
--ptr;
return true;
}
public final String next() {
loadToken();
return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
}
public final String nextLine() {
tokenBuf.clear();
for (int b = readByte(); b != '\n'; b = readByteUnsafe()) {
if (b == -1) break;
tokenBuf.append(b);
}
return new String(tokenBuf.getRawBuf(), 0, tokenBuf.size());
}
public final char nextChar() {
return (char) skipUnprintableChars();
}
public final char[] nextChars() {
loadToken();
return tokenBuf.toCharArray();
}
public final long nextLong() {
long n = 0;
boolean isNegative = false;
int b = skipUnprintableChars();
if (b == '-') {
isNegative = true;
b = readByteUnsafe();
}
if (b < '0' || '9' < b) throw new NumberFormatException();
while ('0' <= b && b <= '9') {
// -9223372036854775808 - 9223372036854775807
if (n >= 922337203685477580l) {
if (n > 922337203685477580l) {
throw new ArithmeticException("long overflow");
}
if (isNegative) {
if (b >= '9') {
throw new ArithmeticException("long overflow");
}
n = -n - (b + '0');
b = readByteUnsafe();
if ('0' <= b && b <= '9') {
throw new ArithmeticException("long overflow");
} else if (b <= 32 || b >= 127) {
return n;
} else {
throw new NumberFormatException();
}
} else {
if (b >= '8') {
throw new ArithmeticException("long overflow");
}
n = n * 10 + b - '0';
b = readByteUnsafe();
if ('0' <= b && b <= '9') {
throw new ArithmeticException("long overflow");
} else if (b <= 32 || b >= 127) {
return n;
} else {
throw new NumberFormatException();
}
}
}
n = n * 10 + b - '0';
b = readByteUnsafe();
}
if (b <= 32 || b >= 127) return isNegative ? -n : n;
throw new NumberFormatException();
}
public final int nextInt() {
long value = nextLong();
if ((int) value != value) {
throw new ArithmeticException("int overflow");
}
return (int) value;
}
public final double nextDouble() {
return Double.parseDouble(next());
}
public final void close() {
try {
in.close();
} catch (java.io.IOException e) {
throw new java.io.UncheckedIOException(e);
}
}
private static final class ByteBuffer {
private static final int DEFAULT_BUF_SIZE = 1 << 12;
private byte[] buf;
private int ptr = 0;
private ByteBuffer(int capacity) {
this.buf = new byte[capacity];
}
private ByteBuffer() {
this(DEFAULT_BUF_SIZE);
}
private ByteBuffer append(int b) {
if (ptr == buf.length) {
int newLength = buf.length << 1;
byte[] newBuf = new byte[newLength];
System.arraycopy(buf, 0, newBuf, 0, buf.length);
buf = newBuf;
}
buf[ptr++] = (byte) b;
return this;
}
private char[] toCharArray() {
char[] chs = new char[ptr];
for (int i = 0; i < ptr; i++) {
chs[i] = (char) buf[i];
}
return chs;
}
private byte[] getRawBuf() {
return buf;
}
private int size() {
return ptr;
}
private void clear() {
ptr = 0;
}
}
}
class TreeBuilder {
private final int n;
private int ptr = 0;
private final int root;
private final SimpleEdge[] edges;
private final int[] count;
public TreeBuilder(int n, int root) {
this.n = n;
this.root = root;
this.edges = new SimpleEdge[n - 1];
this.count = new int[n];
}
public TreeBuilder(int n) {
this(n, 0);
}
public int addEdge(int u, int v, long cost) {
edges[ptr] = new SimpleEdge(u, v, cost);
count[u]++;
count[v]++;
return ptr++;
}
public int addEdge(int u, int v) {
return addEdge(u, v, 1);
}
public SimpleEdge[] getEdges() {
if (ptr < n - 1) throw new NullPointerException("too few edges.");
return edges;
}
public Tree build() {
int[][] adj = new int[n][];
for (int i = 0; i < n; i++) {
adj[i] = new int[count[i]];
}
for (SimpleEdge e : edges) {
int u = e.from;
int v = e.to;
adj[u][--count[u]] = v;
adj[v][--count[v]] = u;
}
return new Tree(n, root, adj);
}
public WeightedTree buildWeightedTree() {
int[][] adj = new int[n][];
long[][] cst = new long[n][];
for (int i = 0; i < n; i++) {
adj[i] = new int[count[i]];
cst[i] = new long[count[i]];
}
for (SimpleEdge e : edges) {
int u = e.from;
int v = e.to;
adj[u][--count[u]] = v;
adj[v][--count[v]] = u;
cst[u][count[u]] = e.cost;
cst[v][count[v]] = e.cost;
}
return new WeightedTree(n, root, adj, cst);
}
}
/**
* @verified
* - http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C
* - https://atcoder.jp/contests/abc014/tasks/abc014_4
*/
class EulerTourLCA {
private final int n;
private final int[] tour;
private final int[] tbeg;
private final int[] dep;
private final int m;
private final int[] seg;
public EulerTourLCA(Tree t) {
this.n = t.getV();
this.tour = new int[2 * n];
this.tbeg = new int[n];
this.dep = new int[n];
dfs(t);
int k = 1;
while (k < n << 1) k <<= 1;
this.m = k;
this.seg = new int[m << 1];
buildSegTree();
}
private void dfs(Tree t) {
int k = 0;
int[] par = t.parent();
int[] stack = new int[n << 1];
int ptr = 0;
int root = t.getRoot();
stack[ptr++] = ~root;
stack[ptr++] = root;
while (ptr > 0) {
int u = stack[--ptr];
if (u >= 0) {
tour[tbeg[u] = k++] = u;
for (int v : t.getEdges(u)) {
if (v == par[u]) continue;
dep[v] = dep[u] + 1;
stack[ptr++] = ~v;
stack[ptr++] = v;
}
} else {
tour[k++] = par[~u];
}
}
}
private void buildSegTree() {
for (int i = 0; i < 2 * n - 1; i++) {
seg[i + m] = dep[tour[i]];
}
java.util.Arrays.fill(seg, m + 2 * n - 1, 2 * m, n);
for (int i = m - 1; i > 0; i--) {
seg[i] = Math.min(seg[i << 1 | 0], seg[i << 1 | 1]);
}
}
public int query(int u, int v) {
if (tbeg[u] > tbeg[v]) return query(v, u);
int mink = -1, min = n;
for (int l = tbeg[u] + m, r = tbeg[v] + m + 1; l < r; l >>= 1, r >>= 1) {
if ((l & 1) == 1) {
if (seg[l] < min) min = seg[mink = l];
l++;
}
if ((r & 1) == 1) {
r--;
if (seg[r] < min) min = seg[mink = r];
}
}
while (mink < m) {
mink <<= 1;
if (min != seg[mink]) mink |= 1;
}
return tour[mink - m];
}
public int dist(int u, int v) {
return dep[u] + dep[v] - 2 * dep[query(u, v)];
}
}
final class SimpleEdge extends AbstractEdge {
public SimpleEdge(int from, int to, long cost) {
super(from, to, cost);
}
public SimpleEdge(int from, int to) {
super(from, to);
}
@Override
public SimpleEdge reverse() {
return new SimpleEdge(to, from, cost);
}
}
abstract class AbstractEdge implements Comparable<AbstractEdge> {
public final int from, to;
public final long cost;
public AbstractEdge(int from, int to, long cost) {
this.from = from;
this.to = to;
this.cost = cost;
}
public AbstractEdge(int from, int to) {
this(from, to, 1l);
}
public abstract AbstractEdge reverse();
public int compareTo(AbstractEdge o) {
return Long.compare(cost, o.cost);
}
}
class WeightedForest extends Forest {
final long[] cst;
final long[][] adjCost;
WeightedForest(int n, int[][] adj, int[][] groups, int[] ids, int[] inv, int[] root, long[][] adjCost) {
super(n, adj, groups, ids, inv, root);
this.cst = new long[n];
this.adjCost = adjCost;
for (int u = 0; u < n; u++) {
int k = adj[u].length;
for (int i = 0; i < k; i++) {
int v = adj[u][i];
long c = adjCost[u][i];
if (v == par[u]) {
cst[u] = c;
} else {
cst[v] = c;
}
}
}
}
public long[] getWeights() {
return cst;
}
public long getWeight(int u, int i) {
return adjCost[u][i];
}
}