Problem Description

Given integers $s, t, u$, where complex numbers $\alpha, \beta, \gamma$ satisfy the following conditions:

• $\alpha + \beta + \gamma = s$
• $\alpha\beta + \beta\gamma + \gamma\alpha = t$
• $\alpha\beta\gamma = u$
• $\alpha, \beta, \gamma$ are distinct.

Given positive integers $n, m$, compute:

\[ \dfrac{\alpha^n(\beta^m-\gamma^m)+\beta^n(\gamma^m-\alpha^m)+\gamma^n(\alpha^m-\beta^m)}{(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)} \]

The answer is guaranteed to be a rational number, so output it modulo $998244353$.

Input Format

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

$n$ $m$ $s$ $t$ $u$

Output Format

Output the answer in one line.

Sample Input and Output

Sample Input #1

2 3
314 159 265

Sample Output #1

159

Sample Input #2

1000000000000000000 800000000000000000
6 11 6

Sample Output #2

76083766

Sample Input #3

1000000000000000000 500000000000000000
505459328 165146837 982639180

Sample Output #3

228155372

Notes/Hints

Notes

When outputting a rational number, first represent it as a fraction $\dfrac{y}{x}$, where $x, y$ are integers and $x$ is not divisible by $998244353$ (under the constraints of this problem, such a representation is always possible). Then, output the unique integer $z$ between $0$ and $998244352$ inclusive that satisfies $\equiv y \pmod{998244353}$.

Constraints

• $1 \leq n \leq 10^{18}$
• $1 \leq m \leq 10^{18}$
• $0 \leq s < 998244353$
• $0 \leq t < 998244353$
• $0 \leq u < 998244353$
• $\alpha, \beta, \gamma$ are distinct.
• All inputs are integers.

见题面 Input 部分

见题面 Output 部分