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 (2.7.1) (judge verdict: Wrong Answer)

n,m,k=gets.split.map(&:to_i)
array=[]
for i in 1..n-1
   
        v=i*m
        array<<v
        if k==v
            puts "Yes"
            exit
        end
    
end

for i in 1..m-1
   
        v=i*n
        array<<v
        if k==v
            puts "Yes"
            exit
        end
    
end
array.uniq!
all_combi=array.combination(2).to_a

plus=all_combi.map{|x,y|x+y}
#p plus
if plus.count(k)!=0
    puts "Yes"
    exit
end

puts "No"