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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function main(input){
    var tmp = input.split(' ');
    var N = Number(tmp[0]);
    var M = Number(tmp[1]);
    var K = Number(tmp[2]);

    var num;
    for(var i=0; i<N; i++){
        for(var j=0; j<M+1; j++){
            num = N*i + M*j - i*j*2;
            if(num==K){
                console.log("Yes");
                return;
            }
        }
    }
    console.log("No");

}

main(require("fs").readFileSync("/dev/stdin", "utf8"));