题目描述

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MainKing has a rooted tree with $n$ nodes, and $m$ paths on it. And the root of this tree is $1$.

The endpoints of the i-th path are $a_i,b_i$. All of these paths satisfy a special condition: $a_i$ is on the path from $b_i$ to the root.

Now MianKing wants to delete all of these paths. He will do the following operator until all of the paths are deleted: choose an integer $x$ from $[1,n]$ randomly and delete all of the paths where $x$ is on.

MianKing wants you to calculate the expected number of operations he need to do.

It's guaranteed that the answer will converge to some rational number.

If the answer is irreducible fraction $\\frac{x}{y}$, you need to output an integer $d$ in $[0,998244352]$ which satisfies $d*y~mod~998244353=x$. It's guaranteed that $y~mod~998244353\ eq 0$

输入格式

The first line has two integers $n,m$.

The second line has $n-1$ integers, the i-th integer denotes the father node of node $i+1$

Then there are $m$ lines, the i-th line has two integers $a_i,b_i$.

$1\\leq n,m\\leq 300$

Let $fa_i$ denote the father node of node $i$. Then $0 \\lt fa_i \\lt i$ for $i \\in [2,n]$

$1\\leq a_i\\leq b_i\\leq n$. It's guaranteed that $a_i$ is on the path from $b_i$ to the root.

输出格式

Output the answer.

样例

3 3 
1 1 
1 2 
3 3 
1 1 

499122181 

提示

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