Problem Statement

Find the number, modulo 998244353, of good sequences of length N whose elements are integers between 0 and M, inclusive, and whose sum is at most K.
Here, $a length-N sequence X=(X_1,X_2,\ldots,X_N)$ is said to be good if and only if there is a graph G that satisfies all of the following conditions.

• G is a graph with N vertices numbered 1 to N without self-loops. (It may have multi-edges.)
• For each i\ $(1\leq i \leq N)$, the degree of vertex i is X_i.
• For each i\ $(1\leq i \leq N)$, no edge connects vertex i and vertex i+1. Here, vertex N+1 means vertex 1.

Input

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

Output

Print the answer.

Constraints

• $4 \leq N \leq 3000$
• $0 \leq M \leq 3000$
• $0\leq K \leq$ NM
• All numbers in the input are integers.

Sample Input 1

4 1 2

Sample Output 1

3

The following three sequences are good.

• (0,0,0,0)
• (0,1,0,1)
• (1,0,1,0)

Sample Input 2

10 0 0

Sample Output 2

1

Sample Input 3

314 159 26535

Sample Output 3

248950743

Print the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分