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"
	"strconv"
)

func main() {
	sc := newScanner()
	N := sc.nextInt()
	M := sc.nextInt()
	K := sc.nextInt()
	ans := false
	fmt.Println("Yes")
	return
	for i := 0; i < N; i++ {
		for j := 0; j < M; j++ {
			black := 0
			black += i * M
			if j > 0 {
				black += j*N - i
			}
			if K == black {
				ans = true
				// log.Println(i, j)
			}
		}
	}
	for i := 0; i < M; i++ {
		for j := 0; j < N; j++ {
			black := 0
			black = i * N
			if j > 0 {
				black += j*M - i
			}
			if K == black {
				ans = true
			}
		}
	}
	if ans {
		fmt.Println("Yes")
	} else {
		fmt.Println("No")
	}
}

func min(a, b int) int {
	if a > b {
		return b
	}
	return a
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

type scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func newScanner() *scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 1000)
	return &scanner{r: rdr}
}
func (s *scanner) next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *scanner) nextLine() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *scanner) nextInt() int {
	v, _ := strconv.Atoi(s.next())
	return v
}
func (s *scanner) nextIntArray() []int {
	s.pre()
	start := s.p
	result := []int{}
	for ; s.p < len(s.buf)+1; s.p++ {
		if s.p == len(s.buf) || s.buf[s.p] == ' ' {
			v, _ := strconv.ParseInt(string(s.buf[start:s.p]), 10, 0)
			result = append(result, int(v))
			start = s.p + 1
		}
	}
	return result
}
func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}