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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

const int N = 110;

int h, w, n;
int b[N][N], a[N * N];

int main() {
	scanf("%d%d", &h, &w);
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) scanf("%d", &a[i]);
	int i = 0, j = 1, d = 1;
	for(int cur = 1; cur <= n; ++cur) {
		while(a[cur]) {
			i += d;
			if(i == h + 1) i = h, ++j, d *= -1;
			else if(!i) i = 1, ++j, d *= -1; 
			b[i][j] = cur;
			--a[cur];
		}
	}
	for(int i = 1; i <= h; ++i) {
		for(int j = 1; j <= w; ++j) printf("%d ", b[i][j]);
		puts("");
	}
	return 0;
}