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 $998244353$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$

Output

Print the answer.

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 $998244353$.