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: Wrong Answer)

# Here your code !
n,m,k=gets.split(' ').map(&:to_i)

a=Array.new(n)
judge=nil
i=0


(n+1).times{
    a[i]=n*i
    i+=1
}

a.each_with_index{|nakami, i|
    h=Array.new(m)
    j=0
    (m+1).times{
        h[j]=nakami+m*j-2*i*j
        j+=1
    }
    if h.include?(k)
        print("Yes")
        judge=true
        break
    else
    end
}

if judge
else
    print("No")
end