Problem Statement

There is an undirected complete graph^† with vertices $1,2,\dots,N$.
Remove exactly $M$ edges from this graph to create a new undirected graph $G$.
In the remaining graph $G$, we want the shortest distance (number of edges traversed) from vertex $1$ to vertex $N$ to be exactly $K$^‡.

Find the number of ways to remove edges that satisfy this condition, modulo $998244353$.
Two ways of removal are considered different if the sets of removed edges are different.

^† An "undirected complete graph" is an undirected graph without self-loops or multiple edges in which exactly $1$ edge exists between any $2$ distinct vertices.
^‡ If vertex $N$ cannot be reached from vertex $1$, the condition is considered not satisfied.

Constraints

• $2 \leq N \leq {\mathbf{35}}$
• $0 \leq M \leq \dfrac{N(N-1)}{2}$
• $1 \leq K \leq N-1$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N\ M\ K$

Output

Print the answer modulo $998244353$ on 1 line.

Sample

4 2 2

5

5 5 4

0

35 520 25

843751679