Problem Statement

You are given a string S of length N consisting of lowercase English letters.
If there are any adjacent occurrences of a and b in S, print Yes; otherwise, print No. (The order of a and b does not matter.)

Constraints

• 2 \leq N \leq 100
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

3
abc

Sample Output 1

Yes

The string abc has a as the first character and b as the second character, which are adjacent. Thus, print Yes.

Sample Input 2

2
ba

Sample Output 2

Yes

The string ba has a as the second character and b as the first character, which are adjacent. (Note that the order of a and b does not matter.)

Sample Input 3

7
atcoder

Sample Output 3

No

Problem Statement

You are given a string S of length N consisting of lowercase English letters, along with lowercase English letters c_1 and c_2.

Find the string obtained by replacing every character of S that is not c_1 with c_2.

Constraints

• 1\le N\le 100
• N is an integer.
• c_1 and c_2 are lowercase English letters.
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

3 b g
abc

Sample Output 1

gbg

Replacing a and c (which are not b) with g in S= abc results in gbg, so print gbg.

Sample Input 2

1 s h
s

Sample Output 2

s

It is possible that the resulting string after replacement is the same as the original string.

Sample Input 3

7 d a
atcoder

Sample Output 3

aaaadaa

Sample Input 4

10 b a
acaabcabba

Sample Output 4

aaaabaabba

Problem Statement

You are given a sequence of M integers A = (A_1, A_2, \dots, A_M).
Each element of A is an integer between 1 and N, inclusive, and all elements are distinct.

List all integers between 1 and N that do not appear in A in ascending order.

Constraints

• All input values are integers.
• 1 \le M \le N \le 1000
• 1 \le A_i \le N
• The elements of A are distinct.

Sample Input 1

10 3
3 9 2

Sample Output 1

7
1 4 5 6 7 8 10

Here, A=(3,9,2).
The integers between 1 and 10 that do not appear in A, listed in ascending order, are 1,4,5,6,7,8,10.

Sample Input 2

6 6
1 3 5 2 4 6

Sample Output 2

0

No integer between 1 and 6 is missing from A.
In this case, print 0 on the first line and leave the second line empty.

Sample Input 3

9 1
9

Sample Output 3

8
1 2 3 4 5 6 7 8

Problem Statement

You are given two grids, each with N rows and N columns, referred to as grid A and grid B.
Each cell in the grids contains a lowercase English letter.
The character at the i-th row and j-th column of grid A is A_{i, j}.
The character at the i-th row and j-th column of grid B is B_{i, j}.

The two grids differ in exactly one cell. That is, there exists exactly one pair (i, j) of positive integers not greater than N such that A_{i, j} \neq B_{i, j}. Find this (i, j).

Constraints

• 1 \leq N \leq 100
• A_{i, j} and B_{i, j} are all lowercase English letters.
• There exists exactly one pair (i, j) such that A_{i, j} \neq B_{i, j}.

Sample Input 1

3
abc
def
ghi
abc
bef
ghi

Sample Output 1

2 1

From A_{2, 1} = d and B_{2, 1} = b, we have A_{2, 1} \neq B_{2, 1}, so (i, j) = (2, 1) satisfies the condition in the problem statement.

Sample Input 2

1
f
q

Sample Output 2

1 1

Sample Input 3

10
eixfumagit
vtophbepfe
pxbfgsqcug
ugpugtsxzq
bvfhxyehfk
uqyfwtmglr
jaitenfqiq
acwvufpfvv
jhaddglpva
aacxsyqvoj
eixfumagit
vtophbepfe
pxbfgsqcug
ugpugtsxzq
bvfhxyehok
uqyfwtmglr
jaitenfqiq
acwvufpfvv
jhaddglpva
aacxsyqvoj

Sample Output 3

5 9

Problem Statement

You are given a string S of length N consisting of lowercase English letters. Each character of S is painted in one of the M colors: color 1, color 2, ..., color M; for each i = 1, 2, \ldots, N, the i-th character of S is painted in color C_i.

For each i = 1, 2, \ldots, M in this order, let us perform the following operation.

• Perform a right circular shift by 1 on the part of S painted in color i. That is, if the p_1-th, p_2-th, p_3-th, \ldots, p_k-th characters are painted in color i from left to right, then simultaneously replace the p_1-th, p_2-th, p_3-th, \ldots, p_k-th characters of S with the p_k-th, p_1-th, p_2-th, \ldots, p_{k-1}-th characters of S, respectively.

Print the final S after the above operations.

The constraints guarantee that at least one character of S is painted in each of the M colors.

Constraints

• 1 \leq M \leq N \leq 2 \times 10^5
• 1 \leq C_i \leq M
• N, M, and C_i are all integers.
• S is a string of length N consisting of lowercase English letters.
• For each integer 1 \leq i \leq M, there is an integer 1 \leq j \leq N such that C_j = i.

Sample Input 1

8 3
apzbqrcs
1 2 3 1 2 2 1 2

Sample Output 1

cszapqbr

Initially, S = apzbqrcs.

• For i = 1, perform a right circular shift by 1 on the part of S formed by the 1-st, 4-th, 7-th characters, resulting in S = cpzaqrbs.
• For i = 2, perform a right circular shift by 1 on the part of S formed by the 2-nd, 5-th, 6-th, 8-th characters, resulting in S = cszapqbr.
• For i = 3, perform a right circular shift by 1 on the part of S formed by the 3-rd character, resulting in S = cszapqbr (here, S is not changed).

Thus, you should print cszapqbr, the final S.

Sample Input 2

2 1
aa
1 1

Sample Output 2

aa

Problem Statement

Takahashi has some letters. Each letter he has is A, B, or C. Initially, he has n _ A letters A, n _ B letters B, and n _ C letters C.

He can hold one contest by using one letter A, one letter C, and additionally any one letter, for a total of three letters. Specifically, he can hold AAC by using two letters A and one letter C, ABC by using one letter each of A, B, and C, and ACC by using one letter A and two letters C.

He wants to hold as many contests as possible using the letters he currently has. Find the maximum number of contests he can hold.

T test cases are given, so report the answer for each of them.

Constraints

• 1\le T\le2\times10 ^ 5
• For each test case,
  • 0\le n _ A\le10 ^ 9
  • 0\le n _ B\le10 ^ 9
  • 0\le n _ C\le10 ^ 9
• All input values are integers.

Sample Input 1

5
3 1 2
100 0 0
1000000 1000000 1000000
31 41 59
1000000000 10000 1

Sample Output 1

2
0
1000000
31
1

In the first test case, he can hold AAC once and ABC once, for a total of two contests. Therefore, output 2 on the first line.

Problem Statement

You are given an integer sequence A=(A_1,A_2,\ldots,A_N) of length N. It is guaranteed that for any i\ (1\le i\le N), A_i is not 0.

Determine whether there exists a permutation B=(B_1,B_2,\ldots,B_N) of A such that B forms a geometric sequence.

A sequence S=(S_1,S_2,\ldots,S_N) is a geometric sequence if there exists a real number r such that S_{i+1}=rS_i for all integers 1\le i\lt N.

Solve T test cases per input file.

Constraints

• 1\le T\le10^5
• 2\le N\le2\times10^5
• -10^9\le A_i\le10^9\ (1\le i\le N)
• A_i\ne0\ (1\le i\le N)
• The sum of N over all test cases in a single input file is at most 2\times10^5.
• All input values are integers.

Sample Input 1

3
5
1 8 2 4 16
5
-16 24 54 81 -36
7
90000 8100 -27000 729 -300000 -2430 1000000

Sample Output 1

Yes
No
Yes

In the first test case, the rearrangement (16,8,4,2,1) of A forms a geometric sequence with common ratio r=\frac{1}{2}. Thus, print Yes on the first line.

In the second test case, no rearrangement of A satisfies the condition. Thus, print No on the second line.

Problem Statement

Given integers A, X, and M, find \displaystyle \sum_{i = 0}^{X-1} A^i, modulo M.

Constraints

• 1 \leq A, M \leq 10^9
• 1 \leq X \leq 10^{12}
• All values in the input are integers.

Sample Input 1

3 4 7

Sample Output 1

5

3^0 + 3^1 + 3^2 + 3^3 = 40, which equals 5 modulo 7, so 5 should be printed.

Sample Input 2

8 10 9

Sample Output 2

0

Sample Input 3

1000000000 1000000000000 998244353

Sample Output 3

919667211

Problem Statement

There are N boxes numbered 1,2,\ldots,N, and 10^{100} balls numbered 1,2,\dots,10^{100}. Initially, box i contains just ball i.

Process a total of Q operations that will be performed.

There are three types of operations: 1, 2, and 3.

Type 1: Put all contents of box Y into box X. It is guaranteed that X \neq Y.

1 X Y

Type 2: Put ball k+1 into box X, where k is the current total number of balls contained in the boxes.

2 X

Type 3: Report the number of the box that contains ball X.

3 X

Constraints

• All values in the input are integers.
• 2 \le N \le 3 \times 10^5
• 1 \le Q \le 3 \times 10^5
• For each type-1 operation, 1 \le X,Y \le N and X \neq Y.
• For each type-2 operation, 1 \le X \le N.
• For each type-3 operation, ball X is contained in some box at that point.
• There is at least one type-3 operation.

Sample Input 1

5 10
3 5
1 1 4
2 1
2 4
3 7
1 3 1
3 4
1 1 4
3 7
3 6

Sample Output 1

5
4
3
1
3

This input contains ten operations.

• The first operation is of type 3. Ball 5 is in box 5.
• The second operation is of type 1. Put all contents of box 4 into box 1.
  • Box 1 now contains balls 1 and 4, and box 4 is now empty.
• The third operation is of type 2. Put ball 6 into box 1.
• The fourth operation is of type 2. Put ball 7 into box 4.
• The fifth operation is of type 3. Ball 7 is in box 4.
• The sixth operation is of type 1. Put all contents of box 1 into box 3.
  • Box 3 now contains balls 1, 3, 4, and 6, and box 1 is now empty.
• The seventh operation is of type 3. Ball 4 is in box 3.
• The eighth operation is of type 1. Put all contents of box 4 into box 1.
  • Box 1 now contains ball 7, and box 4 is now empty.
• The ninth operation is of type 3. Ball 7 is in box 1.
• The tenth operation is of type 3. Ball 6 is in box 3.