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;

#define fo(i,s,t) for(int i = s; i <= t; ++ i)
const int maxn = 105;

int ans[maxn][maxn], n, m, tot, a[maxn*maxn];
int x, y, d;

int main()
{
	scanf("%d%d%d",&n,&m,&tot);
	fo(i,1,tot) scanf("%d",&a[i]);
	x = 1; y = 1; d = 1;
	fo(i,1,tot)
	{
		while(a[i]--)
		{
			ans[x][y] = i;
			if((y == m && d == 1) || (y == 1 && d == -1)) {++ x; d = (d==1?-1:1);}
			else y += d;
		}
	}
	fo(i,1,n) {fo(j,1,m) printf("%d ",ans[i][j]); printf("\n");}
	return 0;
}