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

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

Now MianKing wants to delete all of these paths. He will do the following operation until all of the paths are deleted: choose an integer from randomly and delete all of the paths where 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 , you need to output an integer in which satisfies . It's guaranteed that

The first line has two integers .

The second line has  integers, the i-th integer denotes the father node of node 

Then there are  lines, the i-th line has two integers .



Let  denote the father node of node . Then  for 

. It's guaranteed that  is on the path from  to the root.

Output the answer.

3 3
1 1
1 2
3 3
1 1

499122181