Description

Input

The first line contains three integers $n$, $m$, and $k$ ($1 \leq n, m \leq 1000$, $1 \leq k \leq 10^5$) — the size of the grid and the number of balls dropped by Mr. Chanek.

The $i$-th of the next $n$ lines contains $m$ integers $a_{i,1},a_{i,2},\ldots,a_{i,m}$ ($1 \leq a_{i,j} \leq 3$). It will satisfy $a_{i, 1} \ne 3$ and $a_{i, m} \ne 1$.

The next line contains $k$ integers $c_1, c_2, \ldots, c_k$ ($1 \leq c_i \leq m$) — the balls' column positions dropped by Mr. Chanek sequentially.

Output

Output $k$ integers — the $i$-th integer denoting the column where the $i$-th ball will end.

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

2 2 1

1 2 2
1 3
1 2

1 2

Note

In the first example, the first ball will drop as follows. Note that the cell $(1, 1)$ will change direction to the bottom direction.

The second and third balls will drop as follows.

All balls will be dropped from the first row and on the $c_1, c_2, \dots, c_k$-th columns respectively. A ball will stop dropping once it leaves the grid.