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 Python (3.4.3) (judge verdict: Wrong Answer)

def main():
    """
    0行変更：0
    1行変更：N
    1行変更、1列変更：1つだけ戻る
        N +  M - 2
        (N - 1) + (M - 1)
    2行変更、1列変更：2つだけ戻る
        2N + M - 4
        (2N - 2) + (M - 2)
    2行変更、2列変更：4つだけ戻る
        2N + 2M - 8
        (2N - 4) + (2M - 4)
    """
    N, M, K = map(int, input().split())

    # can = False
    # if K % N == 0 or K % M == 0:
    #     can = True
    for n in range(0, N+1):
        for m in range(0, M+1):
            x = n * N + m * M - (2 * n * m)
            if x == K:
                print("Yes")
                return

    print("No")


if __name__ == '__main__':
    main()