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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strings"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	line := nextLine()
	cols := strings.Split(line," ")
	n,_ := strconv.Atoi(cols[0])
	m,_ := strconv.Atoi(cols[1])
	k,_ := strconv.Atoi(cols[2])
	
	if  n > m {
		n , m = m, n
	}
	mul := m * n
	lesmul := m * (n - 1)
	
	if mul == k {
		fmt.Println("Yes")
	} else if m <= k && k <= lesmul {
		if mul % 2 == 1 && k % 2 == 1 {
			fmt.Println("Yes")
		} else if mul % 2 == 0 && k % 2 == 0 {
			fmt.Println("Yes")
		} else {
			fmt.Println("No")
		}
	} else {
		fmt.Println("No")
	}
	
}