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 <iostream>
#include <vector>
using namespace std;
int main(){
int H,W,N,i,k,x;
cin >> H >> W >> N ;
vector <int> a(N);
for(i=0;i<N;i++){
cin >> a[i];
}
int c[H*W];
	for(k=0;k<a[0];k++){
	c[k] = 1;
	}
	x = 0;
for(i=1;i<N;i++){
	x +=a[i-1];
for(k=0;k<a[i];k++){
	c[x+k] = i+1;
}
}
	i=0;
	while(i!=H*W){
	cout << c[i] <<" ";
		i +=1;
		if(i%W==0 && i!=H*W){
			cout << endl;
			for(k=0;k<W;k++){
				cout << c[i+W-k-1] << " ";
			}
			cout << endl;
		i += W;}
	}
}