Planets Queries II

• Time limit: 1.00 s
• Memory limit: 512 MB

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