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: import javafx.util.Pair;
  
  import java.util.*;
  import java.io.*;
  public class Solution {
  
      public static Pair[][] dp;
      public static int[][] grid;
  
      public static Pair<Integer, Integer> f(int x, int y, int n, int allTwo) {
          if (x > n) {
              return new Pair<>(y, allTwo);
          }
          if (dp[x][y] != null && dp[x][y].getValue().equals(1)) {
              return dp[x][y];
          }
          Pair<Integer, Integer> drop;
          if (grid[x][y] == 1) {
              grid[x][y] = 2;
              drop = f(x, y + 1, n, allTwo & 0);
              return new Pair<>(drop.getKey(), 0);
          } else if (grid[x][y] == 2) {
              grid[x][y] = 2;
              drop = f(x + 1, y, n, allTwo & 1);
              if (drop.getValue() == 0) {
                  return drop;
              }
              return dp[x][y] = drop;
          } else {
              grid[x][y] = 2;
              drop = f(x, y - 1, n, allTwo & 0);
              return new Pair<>(drop.getKey(), 0);
          }
      }
  
      public static void solve(InputReader in, PrintWriter out) {
          int n = in.nextInt();
          int m = in.nextInt();
          int k = in.nextInt();
          grid = new int[n + 1][m + 1];
          dp = new Pair[n + 1][m + 1];
          for (int i = 1; i <= n; i++) {
              for (int j = 1; j <= m; j++) {
                  grid[i][j] = in.nextInt();
              }
          }
          int col;
          while (k-- > 0) {
              col = in.nextInt();
              out.print(f(1, col, n, 1).getKey());
              if (k > 0) {
                  out.print(" ");
              }
          }
          out.println();
      }
  
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          solve(in, out);
          out.close();
      }
      static class InputReader {
          public BufferedReader reader;
          public StringTokenizer tokenizer;
  
          public InputReader(InputStream stream) {
              reader = new BufferedReader(new InputStreamReader(stream), 32768);
              tokenizer = null;
          }
  
          public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
      }
  }