Problem Statement

A 326-like number is a three-digit positive integer where the product of the hundreds and tens digits equals the ones digit.

For example, 326,400,144 are 326-like numbers, while 623,777,429 are not.

Given an integer N, find the smallest 326-like number greater than or equal to N. It always exists under the constraints.

Constraints

• 100 \leq N \leq 919
• N is an integer.

Sample Input 1

320

Sample Output 1

326

320,321,322,323,324,325 are not 326-like numbers, while 326 is a 326-like number.

Sample Input 2

144

Sample Output 2

144

144 is a 326-like number.

Sample Input 3

516

Sample Output 3

600

Problem Statement

Takahashi is exploring a cave in a video game.

The cave consists of N rooms arranged in a row. The rooms are numbered Room 1,2,\ldots,N from the entrance.

Takahashi is initially in Room 1, and the time limit is T.
For each 1 \leq i \leq N-1, he may consume a time of A_i to move from Room i to Room (i+1). There is no other way to move between rooms. He cannot make a move that makes the time limit 0 or less.

There are M bonus rooms in the cave. The i-th bonus room is Room X_i; when he arrives at the room, the time limit increases by Y_i.

Can Takahashi reach Room N?

Constraints

• 2 \leq N \leq 10^5
• 0 \leq M \leq N-2
• 1 \leq T \leq 10^9
• 1 \leq A_i \leq 10^9
• 1 < X_1 < \ldots < X_M < N
• 1 \leq Y_i \leq 10^9
• All values in input are integers.

Sample Input 1

4 1 10
5 7 5
2 10

Sample Output 1

Yes

• Takahashi is initially in Room 1, and the time limit is 10.
• He consumes a time of 5 to move to Room 2. Now the time limit is 5. Then, the time limit increases by 10; it is now 15.
• He consumes a time of 7 to move to Room 3. Now the time limit is 8.
• He consumes a time of 5 to move to Room 4. Now the time limit is 3.

Sample Input 2

4 1 10
10 7 5
2 10

Sample Output 2

No

He cannot move from Room 1 to Room 2.

Problem Statement

There is a 10^{100} \times 7 matrix A, where the (i,j)-th entry is (i-1) \times 7 + j for every pair of integers (i,j)\ (1 \leq i \leq 10^{100}, 1 \leq j \leq 7).

Given an N \times M matrix B, determine whether B is some (unrotated) rectangular part of A.

Constraints

• 1 \leq N \leq 10^4
• 1 \leq M \leq 7
• 1 \leq B_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

2 3
1 2 3
8 9 10

Sample Output 1

Yes

The given matrix B is the top-left 2 \times 3 submatrix of A.

Sample Input 2

2 1
1
2

Sample Output 2

No

Although the given matrix B would match the top-left 1 \times 2 submatrix of A after rotating 90 degrees, the Problem Statement asks whether B is an unrotated part of A, so the answer is No.

Sample Input 3

10 4
1346 1347 1348 1349
1353 1354 1355 1356
1360 1361 1362 1363
1367 1368 1369 1370
1374 1375 1376 1377
1381 1382 1383 1384
1388 1389 1390 1391
1395 1396 1397 1398
1402 1403 1404 1405
1409 1410 1411 1412

Sample Output 3

Yes

Problem Statement

There are N cells numbered from 1 to N in a row. Initially, M cells contain stones, and cell X_i contains A_i stones (1 \leq i \leq M).

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

• If cell i (1 \leq i \leq N-1) contains a stone, move one stone from cell i to cell i+1.

Find the minimum number of operations required to reach a state where each of the N cells contains exactly one stone. If it is impossible, print -1.

Constraints

• 2 \leq N \leq 2 \times 10^{9}
• 1 \leq M \leq 2 \times 10^{5}
• M \leq N
• 1 \leq X_i \leq N (1 \leq i \leq M)
• X_i \neq X_j (1 \leq i < j \leq M)
• 1 \leq A_i \leq 2 \times 10^{9} (1 \leq i \leq M)
• All input values are integers.

Sample Input 1

5 2
1 4
3 2

Sample Output 1

4

You can reach a state where each of the five cells contains exactly one stone with four operations as follows:

• Move one stone from cell 1 to cell 2.
• Move one stone from cell 2 to cell 3.
• Move one stone from cell 4 to cell 5.
• Move one stone from cell 1 to cell 2.

It is impossible to achieve the goal in three or fewer operations. Therefore, print 4.

Sample Input 2

10 3
1 4 8
4 2 4

Sample Output 2

-1

No matter how you perform the operations, you cannot reach a state where all ten cells contain exactly one stone. Therefore, print -1.

Problem Statement

A sequence of n numbers, S = (s_1, s_2, \dots, s_n), is said to be non-decreasing if and only if s_i \leq s_{i+1} holds for every i (1 \leq i \leq n - 1).

Given are non-decreasing sequences of N integers each: A = (a_1, a_2, \dots, a_N) and B = (b_1, b_2, \dots, b_N).
Consider a non-decreasing sequence of N integers, C = (c_1, c_2, \dots, c_N), that satisfies the following condition:

• a_i \leq c_i \leq b_i for every i (1 \leq i \leq N).

Find the number, modulo 998244353, of sequences that can be C.

Constraints

• 1 \leq N \leq 3000
• 0 \leq a_i \leq b_i \leq 3000 (1 \leq i \leq N)
• The sequences A and B are non-decreasing.
• All values in input are integers.

Sample Input 1

2
1 1
2 3

Sample Output 1

5

There are five sequences that can be C, as follows.

• (1, 1)
• (1, 2)
• (1, 3)
• (2, 2)
• (2, 3)

Note that (2, 1) does not satisfy the condition since it is not non-decreasing.

Sample Input 2

3
2 2 2
2 2 2

Sample Output 2

1

There is one sequence that can be C, as follows.

• (2, 2, 2)

Sample Input 3

10
1 2 3 4 5 6 7 8 9 10
1 4 9 16 25 36 49 64 81 100

Sample Output 3

978222082

Be sure to find the count modulo 998244353.