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)

a = gets.chomp.split(" ").map(&:to_i)
n=a[0]
m=a[1]
for i in 0..n
  if a[2] == i + (a[0]-i) * (a[1]-1)
    puts "Yes"
    exit
  end
end
for i in 0..m
  if a[2] == i + (a[1]-i) * (a[0]-1)
    puts "Yes"
    exit
  end
end
puts "No"

#if a[0]-1+a[1]-1 <=a[2] && a[2] <= 1+(a[0]*a[1])
#puts "Yes"
#else
#puts "No"
#end