We have a grid of squares with N rows and M columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left. We will choose K of the squares and put a piece on each of them.

If we place the K pieces on squares (x_1, y_1), (x_2, y_2), ..., and (x_K, y_K), the cost of this arrangement is computed as:

\sum_{i=1}^{K-1} \sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)

Find the sum of the costs of all possible arrangements of the pieces. Since this value can be tremendous, print it modulo 10^9+7.

We consider two arrangements of the pieces different if and only if there is a square that contains a piece in one of the arrangements but not in the other.

Constraints

* 2 \leq N \times M \leq 2 \times 10^5
* 2 \leq K \leq N \times M
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M K


Output

Print the sum of the costs of all possible arrangements of the pieces, modulo 10^9+7.

Examples

Input

2 2 2


Output

8


Input

4 5 4


Output

87210


Input

100 100 5000


Output

817260251
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

import javax.crypto.Cipher;
import javax.naming.InitialContext;

public class Main {
	static final long MOD=1000000007;//998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();
		int K=sc.nextInt();
		long sum=0;
		Binomial binomial=new Binomial();
		for (long i = 1; i < M; i++) {
			long c=M-i;//幅の個数
			long n=((long)N*(long)N)%MOD;
			sum+=(((((c*n)%MOD)*i)%MOD)*binomial.nCk(N*M-2, K-2, MOD))%MOD;
			sum%=MOD;
		}
		for (long i = 1; i < N; i++) {
			long c=N-i;//幅の個数
			long n=((long)M*(long)M)%MOD;
			sum+=(((((c*n)%MOD)*i)%MOD)*binomial.nCk(N*M-2, K-2, MOD))%MOD;
			sum%=MOD;
		}
		System.out.println(sum);
   	}
	static class Binomial{
		int MAX = 510000;//ほしいサイズ
		long[] fac=new long[MAX];
		long[] finv=new long[MAX];
		long[] inv=new long[MAX];
		public Binomial(){
			fac[0] = fac[1] = 1;
		    finv[0] = finv[1] = 1;
		    inv[1] = 1;
		    for (int i = 2; i < MAX; i++){
		        fac[i] = fac[i - 1] * i % MOD;
		        inv[i] = MOD - inv[(int) (MOD%i)] * (MOD / i) % MOD;
		        finv[i] = finv[i - 1] * inv[i] % MOD;
		    }//facがx!、finvがx!の逆元,10^7くらいまでのテーブル(MAXまで)
		}
		long nCk(int n,int k,long MOD) {
		    if (n < k) return 0;
		    if (n < 0 || k < 0) return 0;
		    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
		}
	}
	static long modPow(long x, long y) {
	        long z = 1;
	        while (y > 0) {
	            if (y % 2 == 0) {
	                x = (x * x) % MOD;
	                y /= 2;
	            } else {
	                z = (z * x) % MOD;
	                y--;
	            }
	        }
	        return z;
	    }
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
	}