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

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