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C - Dice Sum /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 1\le A_i \le M (1 \le i \le N)

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

ただし、答えは非常に大きくなることがあるので、答えを 998244353 で割った余りを求めてください。

### 制約

• 1 \leq N, M \leq 50
• N \leq K \leq NM
• 入力は全て整数

### 入力

N M K


### 入力例 1

2 3 4


### 出力例 1

6


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

### 入力例 2

31 41 592


### 出力例 2

798416518


Score : 300 points

### 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


### 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.