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