#include <bits/stdc++.h>
using namespace std;
struct Tree {
  int val;
  Tree* right = NULL;
  Tree* left = NULL;
};
long long int b_expo(long long x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
void solve() {
  long long int n, m, k;
  cin >> n >> m >> k;
  vector<vector<long long int>> a(n + 1, vector<long long int>(m + 1));
  for (long long int i = 1; i < n + 1; i++) {
    for (long long int j = 1; j < m + 1; j++) {
      cin >> a[i][j];
    }
  }
  int v, u, x;
  while (k--) {
    cin >> v;
    u = 1;
    while (u <= n) {
      x = a[u][v];
      a[u][v] = 2;
      if (x == 1) v++;
      if (x == 2) u++;
      if (x == 3) v--;
    }
    cout << v << endl;
  }
}
int main() {
  solve();
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
struct Tree {
  int val;
  Tree* right = NULL;
  Tree* left = NULL;
};
long long int b_expo(long long x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
void solve() {
  long long int n, m, k;
  cin >> n >> m >> k;
  vector<vector<long long int>> a(n + 1, vector<long long int>(m + 1));
  for (long long int i = 1; i < n + 1; i++) {
    for (long long int j = 1; j < m + 1; j++) {
      cin >> a[i][j];
    }
  }
  int v, u, x;
  while (k--) {
    cin >> v;
    u = 1;
    while (u <= n) {
      x = a[u][v];
      a[u][v] = 2;
      if (x == 1) v++;
      if (x == 2) u++;
      if (x == 3) v--;
    }
    cout << v << endl;
  }
}
int main() {
  solve();
  return 0;
}

```