#include <bits/stdc++.h>
const int MOD = 1000000007;
const int MAX = 10000005;
using namespace std;
template <class T>
T max(T a, T b, T c) {
  return max(a, max(b, c));
}
bool prime[1000001];
void SieveOfEratosthenes(int n) {
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
long long fact(long long n) {
  if (n == 0 || n == 1)
    return 1;
  else
    return n * fact(n - 1);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m, k;
  cin >> m >> n >> k;
  long long arr[m][n];
  for (long long i = 0; i < m; i++) {
    for (long long j = 0; j < n; j++) {
      cin >> arr[i][j];
    }
  }
  long long a;
  long long p = 0;
  for (long long i = 0; i < k; i++) {
    cin >> a;
    a--;
    p = 0;
    while (p <= m - 1) {
      if (arr[p][a] == 1) {
        arr[p][a] = 2;
        a++;
      } else if (arr[p][a] == 2) {
        p++;
      } else {
        arr[p][a] = 2;
        a--;
      }
    }
    cout << a + 1 << " ";
  }
}

### 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>
const int MOD = 1000000007;
const int MAX = 10000005;
using namespace std;
template <class T>
T max(T a, T b, T c) {
  return max(a, max(b, c));
}
bool prime[1000001];
void SieveOfEratosthenes(int n) {
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
}
long long fact(long long n) {
  if (n == 0 || n == 1)
    return 1;
  else
    return n * fact(n - 1);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m, k;
  cin >> m >> n >> k;
  long long arr[m][n];
  for (long long i = 0; i < m; i++) {
    for (long long j = 0; j < n; j++) {
      cin >> arr[i][j];
    }
  }
  long long a;
  long long p = 0;
  for (long long i = 0; i < k; i++) {
    cin >> a;
    a--;
    p = 0;
    while (p <= m - 1) {
      if (arr[p][a] == 1) {
        arr[p][a] = 2;
        a++;
      } else if (arr[p][a] == 2) {
        p++;
      } else {
        arr[p][a] = 2;
        a--;
      }
    }
    cout << a + 1 << " ";
  }
}

```