Submission #3968919

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Source Code Expand

#include<iostream>
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<algorithm>
#include<functional>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cassert>
#include<ctime>
using namespace std;

#define mind(a,b) (a>b?b:a)
#define maxd(a,b) (a>b?a:b)
#define absd(x) (x<0?-(x):x)
#define pow2(x) ((x)*(x))
#define rep(i,n) for(int i=0; i<n; ++i)
#define repr(i,n) for(int i=n-1; i>=0; --i)
#define repl(i,s,n) for(int i=s; i<=n; ++i)
#define replr(i,s,n) for(int i=n; i>=s; --i)
#define repf(i,s,n,j) for(int i=s; i<=n; i+=j)
#define repe(e,obj) for(auto e : obj)

#define SP << " " <<
#define COL << " : " <<
#define COM << ", " <<
#define ARR << " -> " <<
#define PNT(STR) cout << STR << endl
#define POS(X,Y) "(" << X << ", " << Y << ")"
#define DEB(A) " (" << #A << ") " << A
#define DEBREP(i,n,val) for(int i=0; i<n; ++i) cout << val << " "; cout << endl
#define ALL(V) (V).begin(), (V).end()
#define INF 1000000007
#define INFLL 1000000000000000007LL
#define EPS 1e-9

typedef unsigned int uint;
typedef unsigned long ulong;
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define P_TYPE int
typedef pair<P_TYPE, P_TYPE> P;
typedef pair<P, P_TYPE> PI;
typedef pair<P_TYPE, P> IP;
typedef pair<P, P> PP;
typedef priority_queue<P, vector<P>, greater<P> > pvqueue;

#define N 3003
#define MOD 1000000007

int n;
int h, w;
int r[N], c[N];
vector<int> g[N];

#define L 100007
ll fact[2*L], rfact[2*L];

ll fast_pow(ll x, ll k) {
  ll r = 1;
  while(k) {
    if(k & 1) {
      r = r * x % MOD;
    }
    x = x * x % MOD;
    k >>= 1;
  }
  return r;
}

ll memo[N];
ll dfs(int v) {
  if(memo[v] != -1) {
    return memo[v];
  }
  ll res = fact[(h - r[v]) + (w - c[v])];
  res = res * rfact[h - r[v]] % MOD;
  res = res * rfact[w - c[v]] % MOD;
  repe(w, g[v]) {
    int dr = r[w] - r[v], dc = c[w] - c[v];
    ll x = fact[dr+dc];
    x = (x * rfact[dr]) % MOD;
    x = (x * rfact[dc]) % MOD;
    res = (res + MOD - (x * dfs(w)) % MOD) % MOD;
  }
  return memo[v] = res;
}

int main() {
  cin >> h >> w >> n;
  rep(i, n) cin >> r[i] >> c[i];
  rep(i, n) {
    rep(j, n) {
      if(i != j && r[i] <= r[j] && c[i] <= c[j]) {
        g[i].push_back(j);
      }
    }
  }
  rep(i, n) memo[i] = -1;
  fact[0] = rfact[0] = 1;
  rep(i, h+w) {
    fact[i+1] = fact[i] * (i+1) % MOD;
    rfact[i+1] = fast_pow(fact[i+1], MOD-2);
  }
  ll ans = fact[h+w-2];
  ans = (ans * rfact[h-1]) % MOD;
  ans = (ans * rfact[w-1]) % MOD;
  rep(i, n) {
    ll x = fact[r[i]+c[i]-2];
    x = (x * rfact[r[i]-1]) % MOD;
    x = (x * rfact[c[i]-1]) % MOD;
    ans = (ans + MOD - (x * dfs(i)) % MOD) % MOD;
  }
  cout << ans << endl;
  return 0;
}

Submission Info

Judge Result