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) {
     input = input.split('\n')
     input.pop()
  input = input[0].split(' ')
    var N = input[0],
        M = input[1],
        K = input[2]
    if ((K % N == 0 && K / N <= M) || (K % M == 0 && K / M <= N)) {
        console.log('Yes')
        return
    }
    if (K < M && K < N) {
        console.log('No')
        return
    }
    for (var i = 1; i <= M; i++) {
        for (var j = 1; j <= N; j++) {
            if (K == (i * M + (N - 2 * j))) {
                console.log('Yes')
                return 
            }
        }
    }
    for (var i = 1; i <= N; i++) {
        for (var j = 1; j <= M; j++) {
            if (K == (i * N + (M - 2 * j))) {
                console.log('Yes')
                return 
            }
        }
    }
    console.log('No')
    return 

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