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)

import random

n, m, k = map(int,input().split(" "))

push_count_n = 0
push_count_m = 0

count = 10000

current = 0

for i in range(count,0,-1):
    if (current == k):
        print("Yes")
        break
    if (current < k and push_count_m <= m):
        push_count_m += 1
        current += m
    elif (current < k and push_count_n <= n):
        push_count_n += 1
        current += n
    else:
        pass


    if (current > k):
        gap = current - k

        strategy = random.randrange(2)

        if strategy == 0:
            if (push_count_n >= n/2 ):
                push_count_m += 1
                current -= n - 2 * push_count_n
        elif (strategy == 1):
            if (push_count_m >= m/2):
                push_count_n += 1
                current -= m - 2 * push_count_m
        else:
            if push_count_m > push_count_n:
                push_count_m -= 1
                current += n - 2 * push_count_n
            else:
                push_count_n -= 1
                current += m - 2 * push_count_m

    if (i == 1):
        print("No")