#include <bits/stdc++.h>
const int N = 100001, M = 998244353, mod = 1000000007;
const long long MX = INT64_MAX, MN = INT64_MIN, oo = 1e18;
using namespace std;
vector<string> tokenizer(string str, char ch) {
  std::istringstream var((str));
  vector<string> v;
  string t;
  while (getline((var), t, (ch))) {
    v.emplace_back(t);
  }
  return v;
}
template <typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& a) {
  in >> a.first >> a.second;
  return in;
}
template <typename T1, typename T2>
ostream& operator<<(ostream& out, pair<T1, T2> a) {
  out << a.first << " " << a.second;
  return out;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
template <typename... T>
void read(T&... args) {
  ((cin >> args), ...);
}
template <typename... T>
void put(T&&... args) {
  ((cout << args << " "), ...);
}
void file_i_o() {
  freopen("./tests/test01.txt", "r", stdin);
  freopen("./tests/output01.txt", "w", stdout);
}
void solve(int T) {
  int n, m, k;
  read(n, m, k);
  vector<vector<int>> grid(n, vector<int>(m));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> grid[i][j];
  while (k--) {
    int c;
    read(c);
    c--;
    int r = 0;
    while (r < n) {
      if (grid[r][c] == 2)
        r++;
      else {
        int nc = c;
        if (grid[r][c] == 1)
          nc++;
        else
          nc--;
        grid[r][c] = 2;
        c = nc;
      }
    }
    put(c + 1);
  }
}
int main(int argc, char const* argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  for (int i = 1; i < t + 1; i++) {
    solve(t);
  }
  return 0;
}

### Prompt

Please create a solution in CPP 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>
const int N = 100001, M = 998244353, mod = 1000000007;
const long long MX = INT64_MAX, MN = INT64_MIN, oo = 1e18;
using namespace std;
vector<string> tokenizer(string str, char ch) {
  std::istringstream var((str));
  vector<string> v;
  string t;
  while (getline((var), t, (ch))) {
    v.emplace_back(t);
  }
  return v;
}
template <typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& a) {
  in >> a.first >> a.second;
  return in;
}
template <typename T1, typename T2>
ostream& operator<<(ostream& out, pair<T1, T2> a) {
  out << a.first << " " << a.second;
  return out;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
template <typename... T>
void read(T&... args) {
  ((cin >> args), ...);
}
template <typename... T>
void put(T&&... args) {
  ((cout << args << " "), ...);
}
void file_i_o() {
  freopen("./tests/test01.txt", "r", stdin);
  freopen("./tests/output01.txt", "w", stdout);
}
void solve(int T) {
  int n, m, k;
  read(n, m, k);
  vector<vector<int>> grid(n, vector<int>(m));
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> grid[i][j];
  while (k--) {
    int c;
    read(c);
    c--;
    int r = 0;
    while (r < n) {
      if (grid[r][c] == 2)
        r++;
      else {
        int nc = c;
        if (grid[r][c] == 1)
          nc++;
        else
          nc--;
        grid[r][c] = 2;
        c = nc;
      }
    }
    put(c + 1);
  }
}
int main(int argc, char const* argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  for (int i = 1; i < t + 1; i++) {
    solve(t);
  }
  return 0;
}

```