After a long and exhausting day of work, Maija decides to visit the local bathhouse. There she finds a gently flowing artificial river filled with pleasantly hot water. She flops into the river and floats wherever the currents take her.

The artificial river can be modeled as n points numbered 1,2,\dots,n, where the i-th point flows to point p_i in one second. Maija's initial position is point 1. There will be q queries numbered 1,2,\dots,q of the following type: find Maija's position a_i seconds after dropping into the river. Note that the river might have loops and dead ends.

Input

The first line contains two integers n and q. The second line contains n integers p_1,\,p_2,\dots,\,p_n. The third line contains q integers a_1,\,a_2,\dots,\,a_q.

Output

Print the answers to the queries on a single line.

Constraints

• 1 \leq n, q \leq 10^5
• 1 \leq p_i \leq n
• 0 \leq a_i \leq 10^{12}

Example 1

Input:

5 5
3 3 4 3 3
12 4 11 0 15

Output:

4 4 3 1 3

Example 2

Input:

10 12
9 4 1 4 2 10 3 7 6 8 
24 7 22 29 0 12 7 0 16 10 99999999999 1000000000000

Output:

10 1 9 9 1 7 1 1 6 10 8 9