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)

N, M, K = map(int, input().split())

if N * M == K:
    print('Yes')
    exit()

for i in range(N):
    for j in range(M):
        print('---')
        print('i：'+str(i))
        print('j：'+str(j))
        print('(N-i)*j：'+str((N-i)*j))
        print('(M-j)*i：'+str((M-j)*i))
        print('目標：'+str(K))
        print('合計：'+str((N-i)*j+(M-j)*i))
        if (N-i)*j+(M-j)*i == K:
            print('Yes')
            exit()
        elif (N-i)*j+(M-j)*i > K:
            break

print('No')