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)

inp = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n')
l = inp.shift().split(' ')
N = l[0] * 1
M = l[1] * 1 
K = l[2] * 1
f = 0
for (i=0; i<N; i++) {
  for (j=0; j<M; j++) {
      if ((M - j) * i + (N - i) * j == K) {
          f = 1
      } 
  }
}
console.log(f ? 'Yes' : 'No')