Problem Statement

In the calendar of AtCoder Kingdom, a year consists of M months from month 1 to month M, and each month consists of D days from day 1 to day D.

What day follows year y, month m, day d in this calendar?

Constraints

• 1000 \leq y \leq 9000
• 1 \leq m \leq M \leq 99
• 1 \leq d \leq D \leq 99
• All input values are integers.

Sample Input 1

12 30
2023 12 30

Sample Output 1

2024 1 1

In the calendar of the kingdom, a year consists of 12 months, and each month consists of 30 days. Thus, the day following year 2023, month 12, day 30 is year 2024, month 1, day 1.

Sample Input 2

36 72
6789 23 45

Sample Output 2

6789 23 46

In the calendar of the kingdom, one year consists of 36 months, and each month consists of 72 days. Thus, the day following year 6789, month 23, day 45 is year 6789, month 23, day 46.

Sample Input 3

12 30
2012 6 20

Sample Output 3

2012 6 21

Problem Statement

Takahashi's purse has one or more 100-yen coins in it and nothing else. (Yen is the Japanese currency.)

Is it possible that the total amount of money in the purse is X yen?

Constraints

• 0 \leq X \leq 1000
• All values in input are integers.

Sample Input 1

500

Sample Output 1

Yes

If the purse has five 100-yen coins, the total amount of money is 500 yen. Thus, it is possible that the total amount is X=500 yen, so we should print Yes.

Sample Input 2

40

Sample Output 2

No

Sample Input 3

0

Sample Output 3

No

Note that the purse has at least one 100-yen coin.

Problem Statement

You are given two strings S and T. Determine whether it is possible to make S and T equal by doing the following operation at most once:

• choose two adjacent characters in S and swap them.

Note that it is allowed to choose not to do the operation.

Constraints

• Each of S and T is a string of length between 2 and 100 (inclusive) consisting of lowercase English letters.
• S and T have the same length.

Sample Input 1

abc
acb

Sample Output 1

Yes

You can swap the 2-nd and 3-rd characters of S to make S and T equal.

Sample Input 2

aabb
bbaa

Sample Output 2

No

There is no way to do the operation to make S and T equal.

Sample Input 3

abcde
abcde

Sample Output 3

Yes

S and T are already equal.

Problem Statement

N students took an exam. The students are labeled as Student 1, Student 2, \dots, Student N, and Student i scored a_i points.

A student who scored less than P points are considered to have failed the exam and cannot earn the credit. Find the number of students who failed the exam.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq P \leq 100
• 0 \leq a_i \leq 100 (1 \leq i \leq N)
• All values in input are integers.

Sample Input 1

4 50
80 60 40 0

Sample Output 1

2

Students 1 and 2, who scored 80 and 60 points, respectively, succeeded in scoring at least 50 points to earn the credit.
On the other hand, Students 3 and 4, who scored 40 and 0 points, respectively, fell below 50 points and failed the exam. Thus, the answer is 2.

Sample Input 2

3 90
89 89 89

Sample Output 2

3

Sample Input 3

2 22
6 37

Sample Output 3

1

Problem Statement

Given an integer N, find the number of integers X that satisfy all of the following conditions, modulo 998244353.

• X is an N-digit positive integer.
• Let X_1,X_2,\dots,X_N be the digits of X from top to bottom. They satisfy all of the following:
  • 1 \le X_i \le 9 for all integers 1 \le i \le N;
  • |X_i-X_{i+1}| \le 1 for all integers 1 \le i \le N-1.

Constraints

• N is an integer.
• 2 \le N \le 10^6

Sample Input 1

4

Sample Output 1

203

Some of the 4-digit integers satisfying the conditions are 1111,1234,7878,6545.

Sample Input 2

2

Sample Output 2

25

Sample Input 3

1000000

Sample Output 3

248860093

Be sure to find the count modulo 998244353.

Problem Statement

You are given six integers: h_1, h_2, h_3, w_1, w_2, and w_3.
Consider writing a positive integer on each square of a 3 \times 3 grid so that all of the following conditions are satisfied:

• For i=1,2,3, the sum of numbers written in the i-th row from the top is h_i.
• For j=1,2,3, the sum of numbers written in the j-th column from the left is w_i.

For example, if (h_1, h_2, h_3) = (5, 13, 10) and (w_1, w_2, w_3) = (6, 13, 9), then all of the following three ways satisfy the conditions. (There are other ways to satisfy the conditions.)

How many ways are there to write numbers to satisfy the conditions?

Constraints

• 3 \leq h_1, h_2, h_3, w_1, w_2, w_3 \leq 30
• All values in input are integers.

Sample Input 1

3 4 6 3 3 7

Sample Output 1

1

The following is the only way to satisfy the conditions. Thus, 1 should be printed.

Sample Input 2

3 4 5 6 7 8

Sample Output 2

0

There may not be a way to satisfy the conditions.

Sample Input 3

5 13 10 6 13 9

Sample Output 3

120

Sample Input 4

20 25 30 22 29 24

Sample Output 4

30613

Problem Statement

You are given a sequence of length N: A=(A_1,A_2,\dots,A_N). The following action on this sequence is called an operation.

• First, choose an integer i such that 1 \le i \le N.
• Next, choose and do one of the following.
  • Add 1 to A_i.
  • Subtract 1 from A_i.

Answer Q questions.
The i-th question is the following.

• Consider performing zero or more operations to change every element of A to X_i. Find the minimum number of operations required to do so.

Constraints

• All values in input are integers.
• 1 \le N,Q \le 2 \times 10^5
• 0 \le A_i \le 10^9
• 0 \le X_i \le 10^9

Sample Input 1

5 3
6 11 2 5 5
5
20
0

Sample Output 1

10
71
29

We have A=(6,11,2,5,5) and three questions in this input.

For the 1-st question, you can change every element of A to 5 in 10 operations as follows.

• Subtract 1 from A_1.
• Subtract 1 from A_2 six times.
• Add 1 to A_3 three times.

It is impossible to change every element of A to 5 in 9 or fewer operations.

For the 2-nd question, you can change every element of A to 20 in 71 operations.

For the 3-rd question, you can change every element of A to 0 in 29 operations.

Sample Input 2

10 5
1000000000 314159265 271828182 141421356 161803398 0 777777777 255255255 536870912 998244353
555555555
321654987
1000000000
789456123
0

Sample Output 2

3316905982
2811735560
5542639502
4275864946
4457360498

The output may not fit into 32-bit integers.

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.

Each square contains an integer. For each i = 1, 2, \ldots, N, the square (r_i, c_i) contains a positive integer a_i. The other square contains a 0.

Initially, there is a piece on the square (R, C). Takahashi can move the piece to a square other than the square it occupies now, any number of times. However, when moving the piece, both of the following conditions must be satisfied.

• The integer written on the square to which the piece is moved is strictly greater than the integer written on the square from which the piece is moved.
• The squares to and from which the piece is moved are in the same row or the same column.

For each i = 1, 2, \ldots, N, print the maximum number of times Takahashi can move the piece when (R, C) = (r_i, c_i).

Constraints

• 2 \leq H, W \leq 2 \times 10^5
• 1 \leq N \leq \min(2 \times 10^5, HW)
• 1 \leq r_i \leq H
• 1 \leq c_i \leq W
• 1 \leq a_i \leq 10^9
• i \neq j \Rightarrow (r_i, c_i) \neq (r_j, c_j)
• All values in input are integers.

Sample Input 1

3 3 7
1 1 4
1 2 7
2 1 3
2 3 5
3 1 2
3 2 5
3 3 5

Sample Output 1

1
0
2
0
3
1
0

The grid contains the following integers.

4 7 0
3 0 5
2 5 5

• When (R, C) = (r_1, c_1) = (1, 1), you can move the piece once by moving it as (1, 1) \rightarrow (1, 2).
• When (R, C) = (r_2, c_2) = (1, 2), you cannot move the piece at all.
• When (R, C) = (r_3, c_3) = (2, 1), you can move the piece twice by moving it as (2, 1) \rightarrow (1, 1) \rightarrow (1, 2).
• When (R, C) = (r_4, c_4) = (2, 3), you cannot move the piece at all.
• When (R, C) = (r_5, c_5) = (3, 1), you can move the piece three times by moving it as (3, 1) \rightarrow (2, 1) \rightarrow (1, 1) \rightarrow (1, 2).
• When (R, C) = (r_6, c_6) = (3, 2), you can move the piece once by moving it as (3, 2) \rightarrow (1, 2).
• When (R, C) = (r_7, c_7) = (3, 3), you cannot move the piece at all.

Sample Input 2

5 7 20
2 7 8
2 6 4
4 1 9
1 5 4
2 2 7
5 5 2
1 7 2
4 6 6
1 4 1
2 1 10
5 6 9
5 3 3
3 7 9
3 6 3
4 3 4
3 3 10
4 2 1
3 5 4
1 2 6
4 7 9

Sample Output 2

2
4
1
5
3
6
6
2
7
0
0
4
1
5
3
0
5
2
4
0

Problem Statement

There is a grid with H rows and W columns. Let (i,j) denote the cell at the i-th row from the top and j-th column from the left.

There are N coins on this grid, and the i-th coin can be picked up by passing through the cell (R_i,C_i).

Your goal is to start from cell (1,1), repeatedly move either down or right by one cell, and reach cell (H,W) while picking up as many coins as possible.

Find the maximum number of coins you can pick up and one of the paths that achieves this maximum.

Constraints

• 2\leq H,W \leq 2\times 10^5
• 1\leq N \leq \min(HW-2, 2\times 10^5)
• 1\leq R_i \leq H
• 1\leq C_i \leq W
• (R_i,C_i)\neq (1,1)
• (R_i,C_i)\neq (H,W)
• (R_i,C_i) are pairwise distinct.
• All input values are integers.

Sample Input 1

3 4 4
3 3
2 1
2 3
1 4

Sample Output 1

3
DRRDR

As shown in the figure above, by moving (1,1)\rightarrow (2,1)\rightarrow (2,2)\rightarrow (2,3)\rightarrow (3,3)\rightarrow (3,4), you can pick up three coins at (2,1),(2,3),(3,3).

Sample Input 2

2 2 2
2 1
1 2

Sample Output 2

1
DR

The path RD is also acceptable.

Sample Input 3

10 15 8
2 7
2 9
7 9
10 3
7 11
8 12
9 6
8 1

Sample Output 3

5
DRRRRRRRRDDDDDRRDRDDRRR