description: 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.
solution: #include <bits/stdc++.h>
  using namespace std;
  vector<vector<int>> grid;
  vector<vector<int>> flag;
  int n, m, k;
  int findFlag(int r, int c) {
    if (flag[r][c] == r || flag[r][c] == n) return flag[r][c];
    flag[r][c] = findFlag(flag[r][c], c);
    return flag[r][c];
  }
  int main() {
    cin >> n >> m >> k;
    grid = vector<vector<int>>(n, vector<int>(m, 0));
    flag = vector<vector<int>>(n, vector<int>(m, 0));
    vector<int> ball(k, 0);
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        cin >> grid[i][j];
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        flag[i][j] = i;
      }
    }
    for (int i = 0; i < k; i++) {
      cin >> ball[i];
      ball[i]--;
    }
    for (int i = 0; i < k; i++) {
      int rCur = 0;
      int cCur = ball[i];
      while (rCur != n) {
        if (grid[rCur][cCur] == 1) {
          grid[rCur][cCur] = 2;
          cCur++;
        } else if (grid[rCur][cCur] == 3) {
          grid[rCur][cCur] = 2;
          cCur--;
        } else {
          int rNew = findFlag(rCur, cCur);
          if (rCur == rNew) {
            flag[rCur][cCur] = rCur + 1;
            rCur++;
          } else
            rCur = rNew;
        }
      }
      cCur++;
      cout << cCur << endl;
    }
    return 0;
  }
  