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 Kotlin (1.3.71) (judge verdict: Accepted)

import kotlin.math.sqrt
 
fun main() {
    val nmk = nextIntList()
    val ans = solve(nmk)
    println(ans)
}
 
fun solve(nmk: List<Int>): String {
    val n = nmk[0]
    val m = nmk[1]
    val k = nmk[2]
 
    val a = (1..n).flatMap { gyou ->
        (1..m).map { retu ->
            val b = gyou * m + retu * (n - gyou) - retu * gyou
            b
        }
    }
  
      val b = a.plus((1..m).map { it * n })

 
    return if(b.contains(k)) {
        "Yes"
    } else {
        "No"
    }
}
 
fun nextIntList(): List<Int> {
    return readLine()!!.split(" ").map { it.toInt() }
}