Description

Given $n$, $a$, and $k$, compute:

Output the answer modulo $998244353$.

Input Format

Input one line with three positive integers $n$, $a$, and $k$.

Output Format

Output one line with one integer representing the answer.

6 4 3

1030980

233333333 114514 1919810

3191086

Hint

Constraints
For $20\%$ of the testdata, $1\le n,k \le 10^5$.
For $100\%$ of the testdata, $1\le k \le 10^7$, $1\le n,a \le 998244352$.

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