#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VL = vector<LL>;
using PII = pair<int, int>;
using PLL = pair<LL, LL>;
void dout() { cerr << endl; }
template <typename Head, typename... Tail>
void dout(Head H, Tail... T) {
  cerr << H << ' ';
  dout(T...);
}
const int MAX = 1 << 10;
int a[MAX][MAX];
set<int> s[MAX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = (0); i < (n); ++i)
    for (int j = (0); j < (m); ++j) {
      cin >> a[i][j];
      if (a[i][j] != 2) s[j].insert(i);
    }
  while (k--) {
    int c;
    cin >> c;
    c--;
    int r = 0;
    while (true) {
      auto it = s[c].lower_bound(r);
      if (it == s[c].end()) break;
      int nr = *it;
      int& na = a[nr][c];
      s[c].erase(it);
      if (na == 1) {
        c++;
      } else {
        assert(na == 3);
        c--;
      }
      na = 2;
      r = nr;
    }
    cout << c + 1 << " ";
  }
  cout << "\n";
}

### Prompt

Please formulate 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;
using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VL = vector<LL>;
using PII = pair<int, int>;
using PLL = pair<LL, LL>;
void dout() { cerr << endl; }
template <typename Head, typename... Tail>
void dout(Head H, Tail... T) {
  cerr << H << ' ';
  dout(T...);
}
const int MAX = 1 << 10;
int a[MAX][MAX];
set<int> s[MAX];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = (0); i < (n); ++i)
    for (int j = (0); j < (m); ++j) {
      cin >> a[i][j];
      if (a[i][j] != 2) s[j].insert(i);
    }
  while (k--) {
    int c;
    cin >> c;
    c--;
    int r = 0;
    while (true) {
      auto it = s[c].lower_bound(r);
      if (it == s[c].end()) break;
      int nr = *it;
      int& na = a[nr][c];
      s[c].erase(it);
      if (na == 1) {
        c++;
      } else {
        assert(na == 3);
        c--;
      }
      na = 2;
      r = nr;
    }
    cout << c + 1 << " ";
  }
  cout << "\n";
}

```