Problem Statement

In the hexadecimal system, where the digits ABCDEF corresponding to 10,11,12,13,14, and 15 are used in addition to 0123456789, every integer between 0 and 255 is represented as a 1- or 2-digit numeral.
For example, 0 and 12 are represented as 1-digit hexadecimal numerals 0 and C; 99 and 255 are represented as 2-digit hexadecimals 63 and FF.

Given an integer N between 0 and 255, convert it to an exactly two-digit hexadecimal numeral, prepending leading 0s if necessary.

Notes

The judge is case-sensitive. Specifically, you cannot use abcdef as hexadecimal digits instead of ABCDEF.

Constraints

• 0 \leq N \leq 255
• N is an integer.

Sample Input 1

99

Sample Output 1

63

99 is represented as 63 in hexadecimal.

Sample Input 2

12

Sample Output 2

0C

12 is represented as C in hexadecimal.
Since we ask you to convert it to a two-digit hexadecimal numeral, the answer is 0C, where 0 is prepended to C.

Sample Input 3

0

Sample Output 3

00

Sample Input 4

255

Sample Output 4

FF

Problem Statement

Print the L-th through R-th characters of the string atcoder.

Constraints

• L and R are integers.
• 1 \le L \le R \le 7

Sample Input 1

3 6

Sample Output 1

code

The 3-rd through 6-th characters of atcoder are code.

Sample Input 2

4 4

Sample Output 2

o

Sample Input 3

1 7

Sample Output 3

atcoder

Problem Statement

You are given N strings S_1,S_2,\dots,S_N of odd lengths consisting of lowercase English letters.

Let m be the length of the longest string among S_1,S_2,\dots,S_N. Find strings T_1,T_2,\dots,T_N satisfying the following condition.

• Condition: T_i is a string of length m formed by concatenating k copies of ., S_i, and k copies of . in this order, for some non-negative integer k.

Constraints

• N is an integer between 1 and 100, inclusive.
• S_i is a string of odd length between 1 and 99, inclusive, consisting of lowercase English letters.

Sample Input 1

4
apple
blueberry
coconut
dragonfruit

Sample Output 1

...apple...
.blueberry.
..coconut..
dragonfruit

m=11, and T_1,T_2,T_3,T_4 satisfy the condition in the problem statement for k=3,1,2,0, respectively.

Sample Input 2

6
abc
d
efghi
jkl
mnopq
r

Sample Output 2

.abc.
..d..
efghi
.jkl.
mnopq
..r..

Problem Statement

You are given an integer sequence A = (A_1, A_2, \dots, A_N) of length N and a positive integer M.

Your goal is to make the following condition false by performing this operation between 0 and N times (inclusive): remove the last element of A.

• Condition: A contains every integer from 1 through M.

Find the minimum number of operations required.

Under the constraints of this problem, it can be proved that it is always possible to make the condition false by performing the operation between 0 and N times.

Constraints

• 1 \le M \le N \le 100
• 1 \le A_i \le M
• All input values are integers.

Sample Input 1

5 3
3 2 3 1 2

Sample Output 1

2

Initially, A = (3,2,3,1,2). Since A contains every integer from 1 through 3, the condition holds.

If you perform the operation once, A = (3,2,3,1). The condition still holds.

If you perform the operation once more, A = (3,2,3). The integer 1 is missing, so the condition no longer holds.

Therefore, the minimum required number of operations is 2.

Sample Input 2

4 3
1 3 1 3

Sample Output 2

0

Since A initially lacks the integer 2, the condition is already false, so no operation is needed.

Sample Input 3

10 4
1 3 3 4 2 1 3 1 2 4

Sample Output 3

6

Problem Statement

You are given an integer N. Consider permuting the digits in N and separate them into two positive integers.

For example, for the integer 123, there are six ways to separate it, as follows:

• 12 and 3,
• 21 and 3,
• 13 and 2,
• 31 and 2,
• 23 and 1,
• 32 and 1.

Here, the two integers after separation must not contain leading zeros. For example, it is not allowed to separate the integer 101 into 1 and 01. Additionally, since the resulting integers must be positive, it is not allowed to separate 101 into 11 and 0, either.

What is the maximum possible product of the two resulting integers, obtained by the optimal separation?

Constraints

• N is an integer between 1 and 10^9 (inclusive).
• N contains two or more digits that are not 0.

Sample Input 1

123

Sample Output 1

63

As described in Problem Statement, there are six ways to separate it:

• 12 and 3,
• 21 and 3,
• 13 and 2,
• 31 and 2,
• 23 and 1,
• 32 and 1.

The products of these pairs, in this order, are 36, 63, 26, 62, 23, 32, with 63 being the maximum.

Sample Input 2

1010

Sample Output 2

100

There are two ways to separate it:

• 100 and 1,
• 10 and 10.

In either case, the product is 100.

Sample Input 3

998244353

Sample Output 3

939337176

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

You are given a string S of length N consisting of 0 and 1.

You can perform the following operation on S any number of times (possibly zero):

• Delete the first or last character, flip it (change 0 to 1 or 1 to 0), and insert it back at any position. More formally, let r(0)= 1 and r(1)= 0, and perform one of the following: (Here, S_i denotes the i-th character of S.)
  • Choose any i\ (1\leq i\leq N) and change S to S_2\dots S_i\,r(S_1)\,S_{i+1}\dots S_N.
  • Choose any i\ (0\leq i\leq N-1) and change S to S_1\dots S_i\,r(S_N)\,S_{i+1}\dots S_{N-1}.

Find the minimum number of operations required to make all characters of S the same. It can be proved that such a sequence of operations always exists.

You are given T test cases, so solve each of them.

Constraints

• 1\leq T\leq 2\times 10^5
• 2\leq N \leq 5\times 10^5
• T and N are integers.
• S is a string of length N consisting of 0 and 1.
• The sum of N over all test cases is at most 5\times 10^5.

Sample Input 1

3
5
01001
3
000
15
110010111100101

Sample Output 1

4
0
16

For the first test case, for example, you can make all characters of S into 0 with four operations as follows. It is impossible to make all characters of S the same with three or fewer operations, so the answer is 4.

• Delete the first character 0, and insert 1 between the 1st and 2nd characters (in S after deletion). S becomes 11001.
• Delete the first character 1, and insert 0 between the 2nd and 3rd characters (in S after deletion). S becomes 10001.
• Delete the last character 1, and insert 0 at the end (in S after deletion). S becomes 10000.
• Delete the first character 1, and insert 0 at the beginning (in S after deletion). S becomes 00000.

For the second test case, all characters of S are the same from the beginning, so no operation is needed.

Problem Statement

You are given a length-N integer sequence A = (A_1, A_2, \ldots, A_N).

Your goal is to perform the following operation repeatedly so that for every length-L contiguous subarray of A, the sum is a multiple of M.

• Choose an integer i such that 1 \leq i \leq N, and increase the value of A_i by 1.

Find the minimum possible number of operations before achieving the goal.

Constraints

• 1 \leq N, M \leq 500
• 1 \leq L \leq N
• 0 \leq A_i < M
• All input values are integers.

Sample Input 1

4 5 3
4 2 1 3

Sample Output 1

4

By performing the operation once choosing i = 2, twice choosing i = 3, and once choosing i = 4, you get A = (4, 3, 3, 4) with a total of four operations, where every length-3 contiguous subarray sums to a multiple of 5.

Sample Input 2

7 10 4
7 0 9 1 6 4 2

Sample Output 2

10

Problem Statement

For a permutation P = (p_1, p_2, \dots, p_N) of (1,2, \dots, N), let us define the score S(P) of P as follows.

• There are N people, numbered 1,2,\dots,N. Additionally, Snuke is there. Initially, Person i (1 \leq i \leq N) has Ball i.
  Each time Snuke screams, every Person i such that i \neq p_i gives their ball to Person p_i simultaneously.
  If, after screaming at least once, every Person i has Ball i, Snuke stops screaming.
  The score is the number of times Snuke screams until he stops. Here, it is guaranteed that the score will be a finite value.

There are N! permutations P of (1,2, \dots, N). Find the sum, modulo 998244353, of the scores of those permutations, each raised to the K-th power.

• Formally, let S_N be the set of the permutations of (1,2, \dots, N). Compute the following: \displaystyle \left(\sum_{P \in S_N} S(P)^K \right) \bmod {998244353}.

Constraints

• 2 \leq N \leq 50
• 1 \leq K \leq 10^4
• All values in input are integers.

Sample Input 1

2 2

Sample Output 1

5

When N = 2, there are two possible permutations P: (1,2),(2,1).

The score of the permutation (1,2) is found as follows.

• Initially, Person 1 has Ball 1, and Person 2 has Ball 2.
  After Snuke's first scream, Person 1 has Ball 1, and Person 2 has Ball 2.
  Here, every Person i has Ball i, so he stops screaming.
  Thus, the score is 1.

The score of the permutation (2,1) is found as follows.

• Initially, Person 1 has Ball 1, and Person 2 has Ball 2.
  After Snuke's first scream, Person 1 has Ball 2, and Person 2 has Ball 1.
  After Snuke's second scream, Person 1 has Ball 1, and Person 2 has Ball 2.
  Here, every Person i has Ball i, so he stops screaming.
  Thus, the score is 2.

Therefore, the answer in this case is 1^2 + 2^2 = 5.

Sample Input 2

3 3

Sample Output 2

79

All permutations and their scores are listed below.

• (1,2,3): The score is 1.
• (1,3,2): The score is 2.
• (2,1,3): The score is 2.
• (2,3,1): The score is 3.
• (3,1,2): The score is 3.
• (3,2,1): The score is 2.

Thus, we should print 1^3 + 2^3 + 2^3 + 3^3 + 3^3 + 2^3 = 79.

Sample Input 3

50 10000

Sample Output 3

77436607