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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

//------------------------------>> tsukasa_diary's template <<------------------------------//
#include <bits/stdc++.h>
using namespace std;

#define for_(i,a,b) for(int i=(a);i<(b);++i)
#define for_rev(i,a,b) for(int i=(a);i>=(b);--i)
#define allof(a) (a).begin(),(a).end()
#define minit(a,b) memset(a,b,sizeof(a))

using lint = long long;
using pii = pair< int, int >;

template< typename T > using Vec = vector< T >;

template< typename T > bool in_range(T x, T lb, T ub) { return lb <= x && x < ub; }
template< typename T > bool in_range(T x, T y, T lb, T ub) { return in_range(x, lb, ub) && in_range(y, lb, ub); }

template< typename T > void modAdd(T& a, T b, T mod) { a = (a + b) % mod; }
template< typename T > void modMul(T& a, T b, T mod) { a = (a * b) % mod; }
template< typename T > void minUpdate(T& a, T b) { a = min(a, b); }
template< typename T > void maxUpdate(T& a, T b) { a = max(a, b); }

int bitCount(int x) { return __builtin_popcount(x); }
int bitCount(lint x) { return __builtin_popcountll(x); }

const int dx[4] = {0,1,0,-1}, dy[4] = {-1,0,1,0};
const int Dx[8] = {0,1,1,1,0,-1,-1,-1}, Dy[8] = {-1,-1,0,1,1,1,0,-1};



//--------------8---------------->> coding space <<-----------------8-------------//

void yes() { puts("Yes"); exit(0); }
void no() { puts("No"); exit(0); }


int main() {
	int N, M, K;
	cin >> N >> M >> K;
	for_(x,0,N+1) {
		int a = x * M;
		for_(y,0,M+1) {
			int b = a + (N-x) * y - x * y;
			if (b == K) yes();
		}
	}
	no();
}
//--------------8---------------->> coding space <<-----------------8-------------//