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: Wrong Answer)

import java.io.PrintWriter;
import java.util.*;


public class Main {
    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        Scanner sc = new Scanner(System.in);
        Task task = new Task();
        task.solve(sc, out);
        out.flush();
        sc.close();
    }

    static class Task {
        void solve(Scanner sc, PrintWriter out) {
            int N = nint(sc);
            int M = nint(sc);
            int K = nint(sc);
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < M; j++) {
                    if (K == i * (M - j) + j * (N - i)){
                        out.println("Yes");
                        return;
                    }
                }
            }
            out.println("No");

        }
    }


    static int nint(Scanner sc) {


        return Integer.parseInt(sc.next());
    }

    static long nlong(Scanner sc) {
        return Long.parseLong(sc.next());
    }

    static double ndouble(Scanner sc) {
        return Double.parseDouble(sc.next());
    }

    static float nfloat(Scanner sc) {
        return Float.parseFloat(sc.next());
    }

    static String nstr(Scanner sc) {
        return sc.next();
    }

    static long[] longLine(Scanner sc, int size) {
        long[] lLine = new long[size];
        for (int i = 0; i < size; i++) {
            lLine[i] = nlong(sc);
        }
        return lLine;
    }

    static int[] intLine(Scanner sc, int size) {
        int[] iLine = new int[size];
        for (int i = 0; i < size; i++) {
            iLine[i] = nint(sc);
        }
        return iLine;
    }

    static String[] strLine(Scanner sc, int size) {
        String[] strLine = new String[size];
        for (int i = 0; i < size; i++) {
            strLine[i] = nstr(sc);
        }
        return strLine;
    }

    static long maxFromList(List<Long> longList) {
        return longList.stream().max(Comparator.naturalOrder()).get();
    }

    static long minFromList(List<Long> longList) {
        return longList.stream().min(Comparator.naturalOrder()).get();
    }

    public static int sumDigits(int n) {
        int sum = 0;
        while (n != 0) {
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }

    public static long sumDigits(long n) {
        long sum = 0;
        while (n != 0) {
            sum += n % 10;
            n /= 10;
        }
        return sum;
    }

    static List<Integer> getIntegerList(Scanner sc, int size) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            list.add(nint(sc));
        }
        return list;
    }

    static List<Long> getLongList(Scanner sc, int size) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            list.add(nlong(sc));
        }
        return list;
    }

    static List<String> getStringList(Scanner sc, int size) {
        List<String> stringList = new ArrayList<>();
        for (int i = 0; i < size; i++) {
            stringList.add(nstr(sc));
        }
        return stringList;
    }

    private static long lcm(long a, long b) {
        return a * b / gcd(b, a % b);
    }

    private static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    private static Map<Integer, Integer> primeFactorize(long num) {
        Map<Integer, Integer> map = new HashMap<>();
        int i = 2;
        while (i * i <= num) {
            while (num % i == 0) {
                num /= i;
                if (map.containsKey(i)) {
                    int tmp = map.get(i);
                    tmp++;
                    map.put(i, tmp);
                } else {
                    map.put(i, 1);
                }
            }
            i++;
        }
        if (num > 1)
            map.put((int) num, 1);
        return map;
    }

    /**
     * Returns the most frequent value in the list. リスト内で最頻出数値を返します。
     *
     * @param list List
     * @return most frequent value
     */
    private static Integer getMode(List<Integer> list) {
        if (list.size() <= 0) {
            throw new IllegalArgumentException();
        }

        Map<Integer, Integer> modeMap = new HashMap<>();

        for (Integer x : list) {
            if (modeMap.containsKey(x)) {
                modeMap.put(x, modeMap.get(x) + 1);
            } else {
                modeMap.put(x, 1);
            }
        }
        return modeMap.entrySet().stream()
                .max(Map.Entry.comparingByValue())
                .get()
                .getKey();

    }
}