Problem:
Score : 200 points

Problem Statement

We have a grid with N rows and M columns of squares. Initially, all the squares are white.

There is a button attached to each row and each column.
When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa.
When a button attached to a column is pressed, the colors of all the squares in that column are inverted.

Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid.

Constraints

1 \leq N,M \leq 1000

0 \leq K \leq NM

Input

Input is given from Standard Input in the following format:

N M K

Output

If Takahashi can have exactly K black squares in the grid, print Yes; otherwise, print No.

Sample Input 1

2 2 2

Sample Output 1

Yes

Press the buttons in the order of the first row, the first column.

Sample Input 2

2 2 1

Sample Output 2

No

Sample Input 3

3 5 8

Sample Output 3

Yes

Press the buttons in the order of the first column, third column, second row, fifth column.

Sample Input 4

7 9 20

Sample Output 4

No

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>

int main(){
		int n,m,k,i,j;
		scanf("%d%d%d",&n,&m,&k);
		int dp[101][101]={0};
		for(i=1;i<=n;i++){
				dp[i][0]=dp[i-1][0]+m;
				for(j=1;j<=m;j++){
						dp[i][j]=dp[i][j-1]+n-i*2;
				}
		}
		int ansf=0;
		for(i=0;i<=n;i++){
				for(j=0;j<=m;j++){
						if(dp[i][j]==k)ansf=1;
				}
		}
		if(ansf==1)puts("Yes");
		else puts("No");
		return 0;
}