A company has n employees, who form a tree hierarchy where each employee has a boss, except for the general director.

Your task is to process q queries of the form: who is employee x's boss k levels higher up in the hierarchy?

Input

The first input line has two integers n and q: the number of employees and queries. The employees are numbered 1,2,\dots,n, and employee 1 is the general director.

The next line has n-1 integers e_2,e_3,\dots,e_n: for each employee 2,3,\dots,n their boss.

Finally, there are q lines describing the queries. Each line has two integers x and k: who is employee x's boss k levels higher up?

Output

Print the answer for each query. If such a boss does not exist, print -1.

Constraints

• 1 \le n,q \le 2 \cdot 10^5
• 1 \le e_i \le i-1
• 1 \le x \le n
• 1 \le k \le n

Example

Input:

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

Output:

3
1
-1