Permutation

A permutation $P$ of size $N$ is an array $P = [P_1, P_2, \dots, P_N]$ with $1 \le P_i \le N$ and $P_i \ne P_j$ for $i \ne j$.

For permutations $A$ and $B$ of size $N$, $A$ is smaller than $B$ when there is an index $i$ ($1 \le i \le N$) such that $A_i < B_i$ and $A_j = B_j$ for all $1 \le j < i$.

For permutations $A$ and $B$ of size $N$, the product $A \times B$ is the permutation of size $N$ whose $i$-th entry is $(A \times B)_i = A_{B_i}$.

For a permutation $P$ and a positive integer $z$, the power $P^z$ is defined by $P^1 = P$ and $P^z = P^{z-1} \times P$ for $z > 1$.

You are given a permutation $P$ of size $N$. Let $M$ be the smallest integer greater than $1$ with $P^M = P$. Let $A_1, A_2, \dots, A_{M-1}$ be $P^1, P^2, \dots, P^{M-1}$ sorted in increasing lexicographic order, so $A_1 < A_2 < \dots < A_{M-1}$.

For instance, if $P = [2, 3, 1, 5, 4]$ then $P^1 = [2, 3, 1, 5, 4]$, $P^2 = [3, 1, 2, 4, 5]$, $P^3 = [1, 2, 3, 5, 4]$, $P^4 = [2, 3, 1, 4, 5]$, $P^5 = [3, 1, 2, 5, 4]$, $P^6 = [1, 2, 3, 4, 5]$ and $P^7 = [2, 3, 1, 5, 4]$. Hence $M = 7$ and the sorted array is $A = [P^6, P^3, P^4, P^1, P^2, P^5]$.

You are also given $Q$ queries. The $i$-th query contains an integer $K_i$. The answer is the integer $T_i$ ($1 \le T_i < M$) with $P^{T_i} = A_{K_i}$. Answer all queries.

The first line contains two integers $N$ and $Q$ ($1 \le N \le 100$, $1 \le Q \le 300000$), the size of the permutation and the number of queries. The second line contains $N$ integers $P_1, P_2, \dots, P_N$ ($1 \le P_i \le N$), the permutation. The input is guaranteed to be a permutation. Each of the next $Q$ lines contains one integer $K_i$ ($1 \le K_i < M$), the query. Here $M$ is the smallest integer greater than $1$ with $P^M = P$ as defined above, and it is not given explicitly in the input.

Print $Q$ lines, each containing one integer $T_i$, the answer to the $i$-th query.

The permutation used in the visible input is the same as the permutation described in the statement.