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 java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class J{
	
	static int n,m;
	static int[][] a,nxt;
	
	static int row,col;
	
	static void upd(int i, int j) {
		a[i][j] = 2;
		if (i == n-1) nxt[i][j] = n;
		else nxt[i][j] = nxt[i+1][j];
		
		if (i != 0) {
			nxt[i-1][j] = nxt[i][j];
		}
	}
	
	static void move() {
	//	System.out.println(row + " " + col);
		if (a[row][col] == 1) {
			upd(row,col);
			col++;
		}
		else if (a[row][col] == 3) {
			upd(row,col);	
			col--;
		}
		else {
			// Move down to next position
			row = nxt[row][col];
		}
	}
	
	public static void main(String[] args) throws IOException{
		// br = new BufferedReader(new FileReader(".in"));
		// out = new PrintWriter(new FileWriter(".out"));
		// new Thread(null, new (), "fisa balls", 1<<28).start();
		
		n =readInt();
		m = readInt();
		a = new int[n][m];
		nxt = new int[n][m];
		int k =readInt();
		for (int[] x: nxt) Arrays.fill(x, n);
		for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = readInt();
		
		for (int j = 0; j < m; j++) {
			for (int i = n-1; i >= 0; i--) {
				if (a[i][j] == 2) {
					if (i == n-1) continue;
					else nxt[i][j] = nxt[i+1][j];
				}
				else nxt[i][j] = i;
			}
		}
		
		
		while(k-->0) {
			row = 0;
			col = readInt()-1;
			while (row < n) move();
			//System.out.println("Done");
			
			out.println(col+1);
		}
		
		out.close();
	}
	
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	static StringTokenizer st = new StringTokenizer("");
	static String read() throws IOException{
		while (!st.hasMoreElements()) st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	public static int readInt() throws IOException{return Integer.parseInt(read());}
	public static long readLong() throws IOException{return Long.parseLong(read());}
}