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 Ruby (2.3.3) (judge verdict: Accepted)

n,m,k = gets.split.map(&:to_i)

(n+1).times do |i|
    if n - 2 * i == 0
        if n * m / 2 == 0 
            puts "Yes"
            exit
        else
            next
        end
    end
    
    j = (k - i * m) / (n - 2 * i)
    if 0 <= j && j <= m && i * (m - j) + (n - i) * j == k
        puts "Yes"
        exit
    end
end

puts "No"