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: Accepted)

var main = function(input) {
var Ar = input.split(' ').map(x=>parseInt(x));
var N=Ar[0];
var M=Ar[1];
var K=Ar[2];
var Ans ='No';
for (var i = 0; i <= N; i++) {
        for (var j = 0; j <= M; j++) {
            if (j * (N - i) + i * (M - j) == K) {
                Ans = 'Yes'
                console.log(Ans);
                return 0;
            }
        }
    }
console.log(Ans);
    return 0; 
}

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