Problem Statement

How many integer sequences of length $N, A=(A_1, \ldots, A_N),$ satisfy all of the conditions below?

• $1\le A_i \le M (1 \le i \le N)$

• $\displaystyle\sum _{i=1}^N A_i \leq K$

Since the count can get enormous, find it modulo 998244353.

Input

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

Output

Print the answer.

Constraints

• $1 \leq N, M \leq 50$
• $N \leq K \leq$ NM
• All values in input are integers.

Sample Input 1

2 3 4

Sample Output 1

6

The following six sequences satisfy the conditions.

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

Sample Input 2

31 41 592

Sample Output 2

798416518

Be sure to print the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分