Problem Statement

You are given a string $S$ of length $N$, a positive integer $M$, and a sequence $K_1,\ldots,K_Q$ of length $Q$.

Let $T$ be the string obtained by repeating the string $S$ $M$ times. When the suffixes $T_1, T_2, \ldots, T_{NM}$ of $T$ are sorted in lexicographical order, find the $K_1,\ldots,K_Q$-th suffixes.

Here, the suffix $T_i$ of $T$ is the substring of $T$ from the $i$-th character to the end.

Input

$N\ M\ Q$
$S$
$K_1\ K_2\ \ldots \ K_Q$

• $N$ is a positive integer satisfying $1\leqq N\leqq 10^5$.
• $M$ is a positive integer satisfying $1\leqq M\leqq 10^9$.
• $Q$ is a positive integer satisfying $1\leqq Q\leqq \min(NM, 10^5)$.
• $S$ is a string of length $N$ consisting of lowercase English letters.
• $K_i$ are positive integers satisfying $1\leqq K_1 < K_2 < \cdots < K_Q \leqq NM$.

Output

For each $i$, find $n_i$ such that the $K_i$-th suffix is $T_{n_i}$, and print them separated by spaces.
Print a newline at the end.

Sample

4 2 8
puyo
1 2 3 4 5 6 7 8

8 4 5 1 6 2 7 3

5 10 4
ahaha
10 20 30 40

5 3 1 4

5 10 4
ihihi
10 20 30 40

7 4 11 8

26 1000000000 1
abcdefghijklmnopqrstuvwxyz
26000000000

26