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)

# -*- coding:utf-8 -*-
n, m, k = map(int, input().split())
factor = []
factor.append(n*m)
for tmp in range(min(n,m)):
    sides = tmp+1
    factor.append(sides**2+((n-sides)*(m-sides)))
factor.append((n//2)*(m//2)*2 + ((((n%2)*m+(m%2)*n)-1)//2 + 1))
if k in factor or k%n == 0 or k%m == 0:
    print("Yes")
else:
    print("No")