Problem Statement

For a length-$N$ sequence of positive integers $A=(A_1,A_2,\dots,A_N)$, define $f(A)$ as follows:

• The maximum value of $A_iA_j + A_k$ over all triples of integers $(i,j,k)$ satisfying $1 \le i < j < k \le N$.

Find the number, modulo $998244353$, of length-$N$ sequences $A$ of positive integers with all elements between $1$ and $M$, inclusive, such that $f(A) \le K$.

Constraints

• $3 \le N \le 10^9$
• $1 \le M,K \le 10^4$

Input

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

N M K

Output

Output the answer.