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)

# Here your c



n,m,k=gets.split
n=n.to_i
m=m.to_i
k=k.to_i


array=[]
i=n
l=0
n.times{
    kk=m*l

     j=0
    (m+1).times{
        array<<kk
        kk=kk+i
        
        
    }
    
  l=l+1  
 i=i-2 
    
}

array=array.sort.uniq


if array.include?(k)

 puts "Yes"
 
 else 
 puts "No"
end