Problem: We have a grid with H rows and W columns of squares. Snuke is painting these squares in colors 1, 2, ..., N. Here, the following conditions should be satisfied:

* For each i (1 ≤ i ≤ N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + ... + a_N = H W.
* For each i (1 ≤ i ≤ N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.



Find a way to paint the squares so that the conditions are satisfied. It can be shown that a solution always exists.

Constraints

* 1 ≤ H, W ≤ 100
* 1 ≤ N ≤ H W
* a_i ≥ 1
* a_1 + a_2 + ... + a_N = H W

Input

Input is given from Standard Input in the following format:


H W
N
a_1 a_2 ... a_N


Output

Print one way to paint the squares that satisfies the conditions. Output in the following format:


c_{1 1} ... c_{1 W}
:
c_{H 1} ... c_{H W}


Here, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.

Examples

Input

2 2
3
2 1 1


Output

1 1
2 3


Input

3 5
5
1 2 3 4 5


Output

1 4 4 4 3
2 5 4 5 3
2 5 5 5 3


Input

1 1
1
1


Output

1

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    int H = scanner.nextInt();
    int W = scanner.nextInt();
    int N = scanner.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++) a[i] = scanner.nextInt();
    for (int i = 1; i < N; i++) a[i] += a[i - 1];
    int[][] res = new int[H][W];
    for (int i = 0; i < H * W; i++) {
      int x = i / W;
      int y = i % W;
      if (x % 2 == 1) y = W - y - 1;
      res[x][y] = lowerBound(a, i + 1) + 1;
    }

    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < H; i++) {
      for (int j = 0; j < W; j++) sb.append(res[i][j]).append(' ');
      sb.setLength(sb.length() - 1);
      sb.append('\n');
    }
    System.out.print(sb.toString());
  }

  public static int lowerBound(int[] a, int k) {
    int left = -1;
    int right = a.length;
    while (right - left > 1) {
      int mid = (left + right) / 2;
      if (k <= a[mid]) {
        right = mid;
      } else {
        left = mid;
      }
    }
    return right;
  }
}