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;

int mp[110][110],x=1,y=1,h,w;

int paint(int color,int area){
	int i;
	for(i=0; i<area; i++){
		 mp[x][y]=color;
		 if(y%2==1){
		 	x++;
		 	if(x>h){
		 		x--;
		 		y++;
		 	}
		 }else{
		 	x--;
		 	if(x<1){
		 		x++;
		 		y++;
		 	}
		 }
	}
	return 0;
}

int main(void){
	int n,i,j,a;
	fill(mp[0],mp[110],0);
	cin >> h >> w >> n;
	for(i=1; i<=n; i++){
		cin >> a;
		paint(i,a);
	}
	for(i=1; i<=h; i++){
		for(j=1; j<w; j++){
			cout << mp[i][j] << " ";
		}
		cout << mp[i][w] << endl;
	}
	return 0;
}