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:
  $\displaystyle \left(\sum_{P \in$ $S_N} S(P)^K \right) \bmod {998244353}$.

Input

Input is given from Standard Input in the following format:
N K

Output

Print $\displaystyle \left(\sum_{P \in$ $S_N} S(P)^K \right) \bmod {998244353}$.

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

见题面 Input 部分

见题面 Output 部分