Planets Queries II

You are playing a game consisting of n planets. Each planet has a teleporter to another planet (or the planet itself). You have to process q queries of the form: You are now on planet a and want to reach planet b. What is the minimum number of teleportations?

Input

The first input line contains two integers n and q: the number of planets and queries. The planets are numbered 1,2,\ldots,n. The second line contains n integers t_1,t_2,\ldots,t_n: for each planet, the destination of the teleporter. Finally, there are q lines describing the queries. Each line has two integers a and b: you are now on planet a and want to reach planet b.

Output

For each query, print the minimum number of teleportations. If it is not possible to reach the destination, print -1.

Constraints

$1 \le n, q \le 2 \cdot 10^5$

$1 \le a,b \le n$

Example

Input

5 3
2 3 2 3 2
1 2
1 3
1 4

Output

1
2
-1