#include <bits/stdc++.h>
using namespace std;
struct Dsu {
  int n, m;
  vector<vector<pair<int, int>>> par;
  Dsu(int n_ = 0, int m_ = 0) : n(n_), m(m_) {
    par = vector<vector<pair<int, int>>>(n, vector<pair<int, int>>(m));
  }
  bool valid(int x, int y) { return min(x, y) >= 0 && min(n - x, m - y) > 0; }
  pair<int, int> get(int u, int v) {
    auto [p, q] = par[u][v];
    assert(valid(u, v) && valid(p, q));
    if (u == p && v == q) return {u, v};
    if (u == p) {
      par[u][v] = valid(u + 1, v) ? make_pair(u + 1, v) : make_pair(u, v);
    } else {
      assert(v == q);
      if (par[p][q].second == v) par[u][v] = par[p][q];
    }
    return get(p, q);
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  Dsu dsu(n, m);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int x, u = i, v = j;
      cin >> x;
      if (x == 1) v++;
      if (x == 2) u++;
      if (x == 3) v--;
      dsu.par[i][j] = dsu.valid(u, v) ? make_pair(u, v) : make_pair(i, j);
    }
  }
  for (int i = 0; i < k; i++) {
    int x;
    cin >> x;
    int k = dsu.get(0, --x).second;
    cout << k + 1 << ' ';
  }
  cout << '\n';
  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 Dsu {
  int n, m;
  vector<vector<pair<int, int>>> par;
  Dsu(int n_ = 0, int m_ = 0) : n(n_), m(m_) {
    par = vector<vector<pair<int, int>>>(n, vector<pair<int, int>>(m));
  }
  bool valid(int x, int y) { return min(x, y) >= 0 && min(n - x, m - y) > 0; }
  pair<int, int> get(int u, int v) {
    auto [p, q] = par[u][v];
    assert(valid(u, v) && valid(p, q));
    if (u == p && v == q) return {u, v};
    if (u == p) {
      par[u][v] = valid(u + 1, v) ? make_pair(u + 1, v) : make_pair(u, v);
    } else {
      assert(v == q);
      if (par[p][q].second == v) par[u][v] = par[p][q];
    }
    return get(p, q);
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  Dsu dsu(n, m);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      int x, u = i, v = j;
      cin >> x;
      if (x == 1) v++;
      if (x == 2) u++;
      if (x == 3) v--;
      dsu.par[i][j] = dsu.valid(u, v) ? make_pair(u, v) : make_pair(i, j);
    }
  }
  for (int i = 0; i < k; i++) {
    int x;
    cin >> x;
    int k = dsu.get(0, --x).second;
    cout << k + 1 << ' ';
  }
  cout << '\n';
  return 0;
}

```