Problem Statement

The ASCII values of the lowercase English letters a, b, \ldots, z are 97,98,\ldots,122 in this order.

Given an integer N between 97 and 122, print the letter whose ASCII value is N.

Constraints

• N is an integer between 97 and 122 (inclusive).

Sample Input 1

97

Sample Output 1

a

97 is the ASCII value of a.

Sample Input 2

122

Sample Output 2

z

Problem Statement

Takahashi is in a building with 100 floors.

He uses the stairs for moving up two floors or less or moving down three floors or less, and uses the elevator otherwise.

Does he use the stairs to move from floor X to floor Y?

Constraints

• 1 \leq X,Y \leq 100
• X \neq Y
• All input values are integers.

Sample Input 1

1 4

Sample Output 1

No

The move from floor 1 to floor 4 involves going up three floors, so Takahashi uses the elevator.

Sample Input 2

99 96

Sample Output 2

Yes

The move from floor 99 to floor 96 involves going down three floors, so Takahashi uses the stairs.

Sample Input 3

100 1

Sample Output 3

No

Problem Statement

There are N weights called Weight 1, Weight 2, \dots, Weight N. Weight i has a mass of A_i.
Let us say a positive integer n is a good integer if the following condition is satisfied:

• We can choose at most 3 different weights so that they have a total mass of n.

How many positive integers less than or equal to W are good integers?

Constraints

• 1 \leq N \leq 300
• 1 \leq W \leq 10^6
• 1 \leq A_i \leq 10^6
• All values in input are integers.

Sample Input 1

2 10
1 3

Sample Output 1

3

If we choose only Weight 1, it has a total mass of 1, so 1 is a good integer.
If we choose only Weight 2, it has a total mass of 3, so 3 is a good integer.
If we choose Weights 1 and 2, they have a total mass of 4, so 4 is a good integer.
No other integer is a good integer. Also, all of 1, 3, and 4 are integers less than or equal to W. Therefore, the answer is 3.

Sample Input 2

2 1
2 3

Sample Output 2

0

There are no good integers less than or equal to W.

Sample Input 3

4 12
3 3 3 3

Sample Output 3

3

There are 3 good integers: 3, 6, and 9.
For example, if we choose Weights 1, 2, and 3, they have a total mass of 9, so 9 is a good integer.
Note that 12 is not a good integer.

Sample Input 4

7 251
202 20 5 1 4 2 100

Sample Output 4

48

Problem Statement

At the entrance of AtCoder Land, there is a single ticket booth where visitors line up to purchase tickets one by one. The purchasing process takes A seconds per person. Once the person at the front of the line finishes purchasing their ticket, the next person (if any) immediately starts their purchasing process.

Currently, there is no one in line at the ticket booth, and N people will come to buy tickets one after another. Specifically, the i-th person will arrive at the ticket booth T_i seconds from now. If there is already a line, they will join the end of it; if not, they will start the purchasing process immediately. Here, T_1 < T_2 < \dots < T_N.

For each i\ (1 \leq i \leq N), determine how many seconds from now the i-th person will finish purchasing their ticket.

Constraints

• 1 \leq N \leq 100
• 0 \leq T_1 < T_2 < \dots < T_N \leq 10^6
• 1 \leq A \leq 10^6
• All input values are integers.

Sample Input 1

3 4
0 2 10

Sample Output 1

4
8
14

The events proceed in the following order:

• At 0 seconds: The 1st person arrives at the ticket booth and starts the purchasing process.
• At 2 seconds: The 2nd person arrives at the ticket booth and joins the line behind the 1st person.
• At 4 seconds: The 1st person finishes purchasing their ticket, and the 2nd person starts the purchasing process.
• At 8 seconds: The 2nd person finishes purchasing their ticket.
• At 10 seconds: The 3rd person arrives at the ticket booth and starts the purchasing process.
• At 14 seconds: The 3rd person finishes purchasing their ticket.

Sample Input 2

3 3
1 4 7

Sample Output 2

4
7
10

The events proceed in the following order:

• At 1 second: The 1st person arrives at the ticket booth and starts the purchasing process.
• At 4 seconds: The 1st person finishes purchasing their ticket, and the 2nd person arrives at the ticket booth and starts the purchasing process.
• At 7 seconds: The 2nd person finishes purchasing their ticket, and the 3rd person arrives at the ticket booth and starts the purchasing process.
• At 10 seconds: The 3rd person finishes purchasing their ticket.

Sample Input 3

10 50000
120190 165111 196897 456895 540000 552614 561627 743796 757613 991216

Sample Output 3

170190
220190
270190
506895
590000
640000
690000
793796
843796
1041216

Problem Statement

There are N stations on a certain line operated by AtCoder Railway. The i-th station (1 \leq i \leq N) from the starting station is named S_i.

Local trains stop at all stations, while express trains may not. Specifically, express trains stop at only M \, (M \leq N) stations, and the j-th stop (1 \leq j \leq M) is the station named T_j.
Here, it is guaranteed that T_1 = S_1 and T_M = S_N, that is, express trains stop at both starting and terminal stations.

For each of the N stations, determine whether express trains stop at that station.

Constrains

• 2 \leq M \leq N \leq 10^5
• N and M are integers.
• S_i (1 \leq i \leq N) is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
• S_i \neq S_j \, (i \neq j)
• T_1 = S_1 and T_M = S_N.
• (T_1, \dots, T_M) is obtained by removing zero or more strings from (S_1, \dots, S_N) and lining up the remaining strings without changing the order.

Sample Input 1

5 3
tokyo kanda akiba okachi ueno
tokyo akiba ueno

Sample Output 1

Yes
No
Yes
No
Yes

Sample Input 2

7 7
a t c o d e r
a t c o d e r

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes
Yes

Express trains may stop at all stations.

Problem Statement

You are given two sequences, each of length N, consisting of integers: A=(A_1, \ldots, A_N) and B=(B_1, \ldots, B_N).

Determine whether there is a sequence of length N, X=(X_1, \ldots, X_N), satisfying all of the conditions below.

• X_i = A_i or X_i = B_i, for every i(1\leq i\leq N).

• |X_i - X_{i+1}| \leq K, for every i(1\leq i\leq N-1).

Constraints

• 1 \leq N \leq 2\times 10^5
• 0 \leq K \leq 10^9
• 1 \leq A_i,B_i \leq 10^9
• All values in input are integers.

Sample Input 1

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

Sample Output 1

Yes

X=(9,6,3,7,5) satisfies all conditions.

Sample Input 2

4 90
1 1 1 100
1 2 3 100

Sample Output 2

No

No X satisfies all conditions.

Sample Input 3

4 1000000000
1 1 1000000000 1000000000
1 1000000000 1 1000000000

Sample Output 3

Yes

Problem Statement

You are given two grids, A and B, each with H rows and W columns.

For each pair of integers (i, j) satisfying 1 \leq i \leq H and 1 \leq j \leq W, let (i, j) denote the cell in the i-th row and j-th column. In grid A, cell (i, j) contains the integer A_{i, j}. In grid B, cell (i, j) contains the integer B_{i, j}.

You will repeat the following operation any number of times, possibly zero. In each operation, you perform one of the following:

• Choose an integer i satisfying 1 \leq i \leq H-1 and swap the i-th and (i+1)-th rows in grid A.
• Choose an integer i satisfying 1 \leq i \leq W-1 and swap the i-th and (i+1)-th columns in grid A.

Determine whether it is possible to make grid A identical to grid B by repeating the above operation. If it is possible, print the minimum number of operations required to do so.

Here, grid A is identical to grid B if and only if, for all pairs of integers (i, j) satisfying 1 \leq i \leq H and 1 \leq j \leq W, the integer written in cell (i, j) of grid A is equal to the integer written in cell (i, j) of grid B.

Constraints

• All input values are integers.
• 2 \leq H, W \leq 5
• 1 \leq A_{i, j}, B_{i, j} \leq 10^9

Sample Input 1

4 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
1 3 2 5 4
11 13 12 15 14
6 8 7 10 9
16 18 17 20 19

Sample Output 1

3

Swapping the fourth and fifth columns of the initial grid A yields the following grid:

1 2 3 5 4
6 7 8 10 9
11 12 13 15 14
16 17 18 20 19

Then, swapping the second and third rows yields the following grid:

1 2 3 5 4
11 12 13 15 14
6 7 8 10 9
16 17 18 20 19

Finally, swapping the second and third columns yields the following grid, which is identical to grid B:

1 3 2 5 4
11 13 12 15 14
6 8 7 10 9
16 18 17 20 19

You can make grid A identical to grid B with the three operations above and cannot do so with fewer operations, so print 3.

Sample Input 2

2 2
1 1
1 1
1 1
1 1000000000

Sample Output 2

-1

There is no way to perform the operation to make grid A match grid B, so print -1.

Sample Input 3

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

Sample Output 3

0

Grid A is already identical to grid B at the beginning.

Sample Input 4

5 5
710511029 136397527 763027379 644706927 447672230
979861204 57882493 442931589 951053644 152300688
43971370 126515475 962139996 541282303 834022578
312523039 506696497 664922712 414720753 304621362
325269832 191410838 286751784 732741849 806602693
806602693 732741849 286751784 191410838 325269832
304621362 414720753 664922712 506696497 312523039
834022578 541282303 962139996 126515475 43971370
152300688 951053644 442931589 57882493 979861204
447672230 644706927 763027379 136397527 710511029

Sample Output 4

20

Problem Statement

Integer Sequence Exhibition is taking place, where integer sequences are gathered in one place and evaluated. Here, every integer sequence of length N consisting of integers between 1 and K (inclusive) is evaluated and given an integer score between 1 and M (inclusive).

Print the number, modulo 998244353, of ways to give each of the evaluated sequences a score between 1 and M.

Here, two ways are said to be different when there is an evaluated sequence A = (A_1, A_2, \ldots, A_N) that is given different scores by the two ways.

Constraints

• 1 \leq N, K, M \leq 10^{18}
• N, K, and M are integers.

Sample Input 1

2 2 2

Sample Output 1

16

Four sequences are evaluated: (1, 1), (1, 2), (2, 1), and (2, 2). There are 16 ways to give each of these sequences a score between 1 and 2, as follows.

• Give 1 to (1, 1), 1 to (1, 2), 1 to (2, 1), and 1 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 1 to (2, 1), and 2 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 2 to (2, 1), and 1 to (2, 2)
• Give 1 to (1, 1), 1 to (1, 2), 2 to (2, 1), and 2 to (2, 2)
• \cdots
• Give 2 to (1, 1), 2 to (1, 2), 2 to (2, 1), and 2 to (2, 2)

Thus, we print 16.

Sample Input 2

3 14 15926535

Sample Output 2

109718301

Be sure to print the count modulo 998244353.

Problem Statement

You are given N linear functions f_1, f_2, \ldots, f_N, where f_i(x) = A_i x + B_i.

Find the maximum possible value of f_{p_1}(f_{p_2}(\ldots f_{p_K}(1) \ldots )) for a sequence p = (p_1, p_2, \ldots, p_K) of K distinct integers between 1 and N, inclusive.

Constraints

• 1 \leq N \leq 2 \times 10^{5}
• 1 \leq K \leq \text{min}(N,10)
• 1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)
• All input values are integers.

Sample Input 1

3 2
2 3
1 5
4 2

Sample Output 1

26

Here are all possible p and the corresponding values of f_{p_1}(f_{p_2}(1)):

• p= ( 1,2 ) : f_1(f_2(1))=15
• p= ( 1,3 ) : f_1(f_3(1))=15
• p= ( 2,1 ) : f_2(f_1(1))=10
• p= ( 2,3 ) : f_2(f_3(1))=11
• p= ( 3,1 ) : f_3(f_1(1))=22
• p= ( 3,2 ) : f_3(f_2(1))=26

Therefore, print 26.

Sample Input 2

10 3
48 40
34 22
24 37
45 40
48 31
49 44
45 40
44 6
35 22
39 28

Sample Output 2

216223