Mr. Chanek has a new game called Dropping Balls. Initially, Mr. Chanek has a grid a of size n × m

Each cell (x,y) contains an integer a_{x,y} denoting the direction of how the ball will move.

  * a_{x,y}=1 — the ball will move to the right (the next cell is (x, y + 1)); 
  * a_{x,y}=2 — the ball will move to the bottom (the next cell is (x + 1, y)); 
  * a_{x,y}=3 — the ball will move to the left (the next cell is (x, y - 1)). 



Every time a ball leaves a cell (x,y), the integer a_{x,y} will change to 2. Mr. Chanek will drop k balls sequentially, each starting from the first row, and on the c_1, c_2, ..., c_k-th (1 ≤ c_i ≤ m) columns.

Determine in which column each ball will end up in (position of the ball after leaving the grid).

Input

The first line contains three integers n, m, and k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 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},…,a_{i,m} (1 ≤ a_{i,j} ≤ 3). It will satisfy a_{i, 1} ≠ 3 and a_{i, m} ≠ 1.

The next line contains k integers c_1, c_2, …, c_k (1 ≤ c_i ≤ 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.

Examples

Input


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


Output


2 2 1 


Input


1 2 2
1 3
1 2


Output


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.

<image>

The second and third balls will drop as follows. 

<image>

All balls will be dropped from the first row and on the c_1, c_2, ..., c_k-th columns respectively. A ball will stop dropping once it leaves the grid.
import javafx.util.Pair;

import java.util.*;
import java.io.*;
public class Solution {

    public static Pair[][] dp;
    public static int[][] grid;

    public static Pair<Integer, Integer> f(int x, int y, int n, int allTwo) {
        if (x > n) {
            return new Pair<>(y, allTwo);
        }
        if (dp[x][y] != null && dp[x][y].getValue().equals(1)) {
            return dp[x][y];
        }
        Pair<Integer, Integer> drop;
        if (grid[x][y] == 1) {
            grid[x][y] = 2;
            drop = f(x, y + 1, n, allTwo & 0);
            return new Pair<>(drop.getKey(), 0);
        } else if (grid[x][y] == 2) {
            grid[x][y] = 2;
            drop = f(x + 1, y, n, allTwo & 1);
            if (drop.getValue() == 0) {
                return drop;
            }
            return dp[x][y] = drop;
        } else {
            grid[x][y] = 2;
            drop = f(x, y - 1, n, allTwo & 0);
            return new Pair<>(drop.getKey(), 0);
        }
    }

    public static void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        grid = new int[n + 1][m + 1];
        dp = new Pair[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                grid[i][j] = in.nextInt();
            }
        }
        int col;
        while (k-- > 0) {
            col = in.nextInt();
            out.print(f(1, col, n, 1).getKey());
            if (k > 0) {
                out.print(" ");
            }
        }
        out.println();
    }

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}