In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled.

Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game.

Input

The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000).

Output

Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7).

Examples

Input

3 3 1


Output

1


Input

4 4 1


Output

9


Input

6 7 2


Output

75

Note

Two ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way.

In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square.

In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square.
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.flush();
		out.close();
	}
}

class Pair implements Comparable<Pair> {
	int first;
	int second;

	Pair(int first, int second) {
		this.first = first;
		this.second = second;
	}

	@Override
	public int compareTo(Pair e) {
		return Long.compare(second, e.second);

	}
}

class TaskB {
	int INF = (int) 1e9 + 7;
	int MAX_N = (int) 1e5 + 5;
	long mod = (long) 1e8;

	void solve(int testNumber, InputReader in, PrintWriter pw) {
		int rowCount = in.nextInt();
		int columnCount = in.nextInt();
		int stepCount = in.nextInt();
		if (rowCount == 1 || columnCount == 1) {
			pw.println(0);
			return;
		}
		long[][] count = new long[stepCount + 1][Math.max(rowCount, columnCount) + 1];
		for (int i = 0; i < count[1].length; i++)
			count[1][i] = i * (i + 1) / 2;
		for (int i = 2; i <= stepCount; i++) {
			long sum = 0;
			long res = 0;
			for (int j = 2; j < count[i].length; j++) {
				sum += count[i - 1][j - 2];
				res += sum;
				res %= INF;
				count[i][j] = res;
//				pw.println(i + " " + j + " " + res + " " + sum);
			}
		}
		long answer = count[stepCount][rowCount - 2] * count[stepCount][columnCount - 2] % INF;
		pw.println(answer);

	}

	int dist(int[] x, int[] y) {
		return (x[0] - y[0]) * (x[0] - y[0]) + (x[1] - y[1]) * (x[1] - y[1]);

	}

	long gcd(long a, long b) {
		if (b == 0) {
			return a;
		} else {
			return gcd(b, a % b);
		}
	}

	int[] shrink(int a[]) {
		int n = a.length;
		long b[] = new long[n];
		for (int i = 0; i < n; i++) {
			b[i] = ((long) (a[i] << 32)) | i;
		}
		Arrays.sort(b);
		int ret[] = new int[n];
		int p = 0;
		for (int i = 0; i < n; i++) {
			if (i > 0 && (b[i] ^ b[i - 1]) >> 32 != 0) {
				p++;
			}
			ret[(int) b[i]] = p;
		}
		return ret;
	}

	int sum(int ft[], int i) {
		int sum = 0;
		for (int j = i; j >= 1; j -= (j & -j)) {
			sum += ft[j];
//			System.out.println(sum);
		}
		return sum;
	}

	void add(int ft[], int i, int x) {
		for (int j = i; j < ft.length; j += (j & -j)) {
//			System.out.println(j);
			ft[j] += x;
		}
	}

	boolean isValid(int i, int j, char arr[][]) {

		if (i >= arr[0].length || j >= arr[0].length) {
			return false;
		}
		if (arr[i][j] == '*') {
			return false;
		}
		return true;
	}

	long pow(long m, long k) {
		long prod = 1;
		for (int i = 0; i < k; i++) {
			prod = (prod * m) % INF;
		}
		return prod % INF;
	}

//	int sum(int k) {
//		int sum=0;
//		for(int i=k;i>=1;i) {
//			sum+=ft[k];
//		}
//	}

	long fib(int N) {
		long fib[] = new long[N + 1];
		fib[0] = 1;
		fib[1] = 1;
		for (int i = 2; i <= N; i++) {
			fib[i] = (fib[i - 1] + fib[i - 2]) % mod;
		}
		return fib[N] % mod;
	}

	long sum(int i, int j, long arr[]) {
		long sum = 0;
		for (int k = i; k <= j; k++) {
			sum += arr[k];
		}
		return sum;
	}

	int __gcd(int a, int b) {
		if (b == 0)
			return a;
		return __gcd(b, a % b);

	}

	public int isPow(long num) {
		int count = 0;
		while (num > 0) {
			num /= 2;
			count++;
		}
		return count;
	}
}

class InputReader {
	BufferedReader br;
	StringTokenizer st;

	public InputReader(InputStream in) {
		br = new BufferedReader(new InputStreamReader(in));
		st = null;
	}

	public String next() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}