24660번 - High Powers 다국어

문제

Given are integers $s,ドル $t,ドル and $u$.

Let $a,ドル $b,ドル and $c$ be distinct complex numbers that satisfy the following conditions:

• $a+b+c=s,ドル
• $ab + bc + ca=t,ドル
• $abc=u$.

It is guaranteed that such $a,ドル $b,ドル and $c$ exist for the given $s,ドル $t,ドル and $u$.

Given positive integers $n$ and $m,ドル calculate the ratio

$$ \frac{a^n(b^m-c^m)+b^n(c^m-a^m)+c^n(a^m-b^m)}{(a-b)(b-c)(c-a)} $$

modulo 998ドル,244円,353円$.

입력

The first line of input contains two integers $n$ and $m$ (1ドル \le n, m \le 10^{18}$).

The second line contains three integers $s,ドル $t$ and $u$ (0ドル \le s, t, u < 998,244円,353円$).

It is guaranteed that the distinct complex numbers $a,ドル $b,ドル and $c$ from the statement exist for the given $s,ドル $t,ドル and $u$.

출력

It can be shown that the answer can be represented as a rational number $p/q$ where $p$ and $q$ are integers, $(p,q)=1,ドル $q>0$ and $q$ is not divisible by 998ドル,244円,353円$.

제한

힌트