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.Arrays;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main{
	static Scanner s=new Scanner(System.in);
	static IntStream REPS(int v){return IntStream.range(0,v);}
	static IntStream REPS(int l,int r){return IntStream.rangeClosed(l,r);}
	static IntStream INS(int n) {return REPS(n).map(i->getInt());}
	static int getInt(){return Integer.parseInt(s.next());}
	static class Pair<T,U>{
		T l;U r;
		Pair(T L,U R){l=L;r=R;}
		T getL(){return l;}
		U getR(){return r;}
	}


	static final int h=getInt(),w=getInt(),n=getInt(),a[]=INS(n).toArray();
	public static void main(String[]$){

		if(w==1) {
			for(int i=0;i<n;++i) {
				for(int j=0;j<a[i];++j) {
					System.out.println(i+1);
				}
			}
			return;
		}

		int[][]f=new int[h][w];
		Arrays.stream(f).forEach(o->Arrays.fill(o,-1));
		int x=0,y=0,dx=1,dy=0;
		int color=0;
		try {
			while(true){
				--a[color];
				f[y][x]=color+1;
				if(a[color]==0)++color;

				x+=dx;y+=dy;

				if(x==w-1) {
					if(y%2==0) {
						dx=0;
						dy=1;
					}else {
						dx=-1;
						dy=0;
					}
				}
				if(x==0) {
					if(y%2==1){
						dx=0;
						dy=1;
					}else {
						dx=1;
						dy=0;
					}
				}
			}
		}catch (Exception e) {
		}
		Arrays.stream(f).map(
				o->Arrays.stream(o)
				.mapToObj(String::valueOf)
				.collect(Collectors.joining(" "))
				).forEach(System.out::println);
	}
}