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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Set;

public class Main implements Runnable {
    public static void main(String[] args) {
        new Thread(null,new Main(), "" ,Runtime.getRuntime().maxMemory()).start();
    }

    // メイン処理
    public void run() {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        
        boolean exist = false;
        for(int i = 0;i <= n;i++) {
            for(int j = 0;j <= m;j++) {
                int tmp = m * i + n * j - 2 * i * j;
                if(tmp == k) {
                    exist = true;
                    break;
                }
            }
            
            if(exist) break;
        }
        
        PrintWriter out =  new PrintWriter(System.out);
        if(exist) out.println("Yes");
        else out.println("No");
        out.flush();
    }

    // 以下、ユーティリティ
    // n以上となる最小のインデックスを返す
    int binarySearch(int[] l, int n) {
        int left = -1;
        int right = l.length;
        while(right - left > 1) {
            int middle = left + (right - left) / 2;
            if(l[middle] >= n) right = middle;
            else left = middle;
        }

        return right;
    }

    Set<long[]> primeFactorize(long n){
        // たとえnが10^18でも約数の個数は400を超えないため素因数はもっと少なくなる
        Set<long[]> ret = new HashSet<>(500);
        for(long p = 2;p * p <= n;p++) {
            if(n % p != 0) continue;
            long num = 0;
            while(n % p == 0) {
                ++num;
                n /= p;
            }
            long[] arr = {p, num};
            ret.add(arr);
        }
        if(n != 1) {
            long[] arr = {n, 1};
            ret.add(arr);
        }

        return ret;
    }

    // nの約数を求める
    Set<Long> searchDivisor(long n){
        Set<Long> ret = new HashSet<>(200);
        for(long i = 1;i * i <= n;i++) {
            if(n % i == 0) {
                ret.add(Long.valueOf(i));
                if(i * i != n) ret.add(Long.valueOf(n / i));
            }
        }

        return ret;
    }

    Set<Integer> searchDivisor(int n){
        Set<Integer> ret = new HashSet<>(200);
        for(int i = 1;i * i <= n;i++) {
            if(n % i == 0) {
                ret.add(Integer.valueOf(i));
                if(i * i != n) ret.add(Integer.valueOf(n / i));
            }
        }

        return ret;
    }

    // 素数判定
    public static boolean isPrime(long num) {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false;

        double sqrtNum = Math.sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2) {
            if (num % i == 0) return false;
        }

        return true;
    }

    long nCm(long n, long m) {
        if(n < m) return 0l;
        long c = 1l;
        m = (n - m < m ? n - m : m);
        for(long ns = n - m + 1, ms = 1;ms <= m;ns ++, ms++) {
            c *= ns;
            c /= ms;
        }
        return c;
    }

    long modnCm(long n, long m, long mod) {
        if(n < m) return 0l;
        long upper = 1l;
        long downer = 1l;
        m = (n - m < m ? n - m : m);
        for(long ns = n - m + 1, ms = 1;ms <= m;ns ++, ms++) {
            upper = upper * ns % mod;
            downer = downer * ms % mod;
        }
        return upper * modInv(downer, mod) % mod;
    }

    // mod m での a の逆元 を計算する
    long modInv(long a, long m) {
        long b = m, u = 1, v = 0;
        while(b > 0) {
            long t = a / b;
            a -= t * b;
            long tmp = a;
            a = b;
            b = tmp;
            u -= t * v;
            tmp = u;
            u = v;
            v = tmp;
        }
        u %= m;
        if (u < 0) u += m;
        return u;
    }

    long modPow(long a, long n, long mod) {
        long res = 1l;
        while(n > 0l) {
            if(n % 2l == 1l) res = res * a % mod;
            a = a * a % mod;
            n /= 2l;
        }
        return res;
    }

}

class UnionFind {
    protected int[] parent;

    UnionFind(int n) {
        parent = new int[n];
        for(int i = 0;i < n;i++) parent[i] = i;
    }

    public int rootOf(int x) {
        if(parent[x] == x) return x;
        else return parent[x] = rootOf(parent[x]);
    }

    public boolean same(int x, int y) {
        return rootOf(x) == rootOf(y);
    }

    public void unite(int x, int y) {
        x = rootOf(x);
        y = rootOf(y);
        if(x == y) return;
        parent[x] = y;
        return;
    }
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}