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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<cstdint>
#include<cstddef>
#include<set>
using namespace std;
using i32 = int_fast32_t;
using i64 = int_fast64_t;
using usize = uint_fast64_t;
#define rep(i, n) for (usize i = 0; i < (usize)(n); i++)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
using P = pair<i64,i64>;

int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    usize n,m,k;
    cin >> n >> m >> k;
    set<usize> st;
    st.insert(n * m);
    for(usize i = 1; i <= n;/*たて*/ i++){
        for(usize j = 1; j <= m;/*よこ*/ j++){
            st.insert(j*(m - j) + (n - i) * n);
        }
    }
    cout << (st.count(k) ? "Yes" : "No") << endl;
}