#include <bits/stdc++.h>
using namespace std;
void solve() {
  long long int n, m, k;
  cin >> n >> m >> k;
  long long int a[n][m];
  long long int res[n][m];
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < m; j++) {
      cin >> a[i][j];
    }
  }
  long long int c[k];
  for (long long int i = 0; i < k; i++) {
    cin >> c[i];
  }
  for (long long int i = 0; i < k; i++) {
    long long int x = 0, y = c[i] - 1;
    while (x < n) {
      if (a[x][y] == 1) {
        y++;
        a[x][y - 1] = 2;
        continue;
      }
      if (a[x][y] == 2) {
        x++;
        continue;
      }
      if (a[x][y] == 3) {
        y--;
        a[x][y + 1] = 2;
        continue;
      }
    }
    cout << y + 1 << " ";
  }
  cout << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void solve() {
  long long int n, m, k;
  cin >> n >> m >> k;
  long long int a[n][m];
  long long int res[n][m];
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < m; j++) {
      cin >> a[i][j];
    }
  }
  long long int c[k];
  for (long long int i = 0; i < k; i++) {
    cin >> c[i];
  }
  for (long long int i = 0; i < k; i++) {
    long long int x = 0, y = c[i] - 1;
    while (x < n) {
      if (a[x][y] == 1) {
        y++;
        a[x][y - 1] = 2;
        continue;
      }
      if (a[x][y] == 2) {
        x++;
        continue;
      }
      if (a[x][y] == 3) {
        y--;
        a[x][y + 1] = 2;
        continue;
      }
    }
    cout << y + 1 << " ";
  }
  cout << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
}

```