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)

#include <bits/stdc++.h>
using namespace std;

#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define REP(i, n)  for(int i=0;i<(n);++i)
#define REPr(i, n) for(int i=(n)-1;i>=0; --i)
#define FORq(i, m, n) for(int i = (m);i <= (n);++i)
#define FORqr(i, m, n) for(int i = (n);i >=(m);--i)
#define PB push_back
#define MP make_pair
#define fst first
#define snd second
#define SIN(x, S) (S.count(x) != 0)
#define M0(x) memset(x,0,sizeof(x))
#define FILL(x, y) memset(x,y,sizeof(x))
#define MM(x) memset(x,-1,sizeof(x))
#define ALL(x) (x).begin(),(x).end()
#define DB(x) cerr << #x << " = " << x << endl
#define DB2(x, y) cerr << "(" << #x << ", " << #y << ") = (" << x << ", " << y << ")\n";
#define DEBUG int x12345; cin >> x12345;
typedef pair<int, int> PII;
typedef pair<long long, long long> PLL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<long long> VL;
typedef long long ll;
typedef long long integer;
///////////////////////////////////////////////
const ll MOD = 1e9 + 7;
ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
 
template<class T>
inline bool chmin(T &a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
 
template<class T>
inline bool chmax(T &a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}
 
template<int MOD>
struct Fp {
	long long val;
 
	constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
		if (val < 0) v += MOD;
	}
 
	constexpr int getmod() { return MOD; }
 
	constexpr Fp operator-() const noexcept {
		return val ? MOD - val : 0;
	}
 
	constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; }
 
	constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; }
 
	constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; }
 
	constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; }
 
	constexpr Fp &operator+=(const Fp &r) noexcept {
		val += r.val;
		if (val >= MOD) val -= MOD;
		return *this;
	}
 
	constexpr Fp &operator-=(const Fp &r) noexcept {
		val -= r.val;
		if (val < 0) val += MOD;
		return *this;
	}
 
	constexpr Fp &operator*=(const Fp &r) noexcept {
		val = val * r.val % MOD;
		return *this;
	}
 
	constexpr Fp &operator/=(const Fp &r) noexcept {
		long long a = r.val, b = MOD, u = 1, v = 0;
		while (b) {
			long long t = a / b;
			a -= t * b;
			swap(a, b);
			u -= t * v;
			swap(u, v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
 
	constexpr bool operator==(const Fp &r) const noexcept {
		return this->val == r.val;
	}
 
	constexpr bool operator!=(const Fp &r) const noexcept {
		return this->val != r.val;
	}
 
	friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept {
		return os << x.val;
	}
 
	friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept {
		return is >> x.val;
	}
 
	friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
		if (n == 0) return 1;
		auto t = modpow(a, n / 2);
		t = t * t;
		if (n & 1) t = t * a;
		return t;
	}
};
 
using mint = Fp<MOD>;
 
void scdvec(vector<int> &a, int n, int s = 0) {
	for (int i = s; i < n; ++i) { scanf("%d", &a[i]); }
}
 
void sclldvec(vector<long long> &a, int n, int s = 0) {
	for (int i = s; i < n; ++i) { scanf("%lld", &a[i]); }
}
 
///////////////////////////////////////////////
///  ((((っ・ω・)っ |AC|
int main(){
	int N,M,K;
	cin >> N >> M >> K;
	bool ok = false;
	FORq(i,0,M){
		FORq(j,0,N){
			int black = 0;
			black += i * N;
			black += j * M;
			black -= i * j * 2;
			if (black == K) ok = true;
		}
	}
	if (ok) cout << "Yes" << endl;
	else cout << "No" << endl;
}