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.util.NoSuchElementException;

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 nextDoutble(){return Double.parseDouble(next());}
}
class MOD {
    static long[] fac,inv,finv;
    static int mod = 1000000007;

    public static long getPowMod(long a, long x,long mod){
        long res = 1;
        while(x > 0){
            if((x&1)==1){
                res = (res*a)%mod;
            }
            x>>=1;
            a = (a*a)%mod;
        }
        return res;
    }
    public static long getFactorialMod(long n,long mod){
        if(n==0){
            return 1;
        }else{
            return (n*getFactorialMod(n-1, mod))%mod;
        }
    }

    public static long nCkMod(long n,long k,long mod){
        if(n < k){
            return 0;
        }else{
            long nMod = getFactorialMod(n, mod);
            long kinvMod = getPowMod(getFactorialMod(k, mod), mod-2, mod);
            long n_kinvMod = getPowMod(getFactorialMod(n-k, mod), mod-2, mod);
            long x = (nMod*kinvMod)%mod;
            return (x*n_kinvMod)%mod;
        }
    }

    public static void COMinit(int max){
        fac = new long[max];
        inv = new long[max];
        finv = new long[max];
        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[mod%i]*(mod/i)%mod;
            finv[i] = finv[i-1]*inv[i]%mod;
        }
    }
    public static long nCkMod2(int n,int k){
        if(n < k)return 0;
        return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
    }
    public static long getInv(int n){
        return inv[n];
    }
}
public class Main {
    public static void main(String[] args) {
        FastScanner fs= new FastScanner();
        int n = fs.nextInt();
        int m = fs.nextInt();
        int k = fs.nextInt();
        long[][] dp = new long[n][m];
        int mod = 1000000007;
        dp[0][0] = (long)m*n*(m+n-2)/2;
        dp[0][0] %= mod;
        
        MOD.COMinit(300000);

        long sum = dp[0][0];
        
        for(int i=0;i<n;i++){
            if(i > 0){
                dp[i][0] = (dp[i-1][0] + i*m - m*(n-i)+mod)%mod;
                sum+=dp[i][0];
            }
            for(int j=1;j<m;j++){
                dp[i][j] = (dp[i][j-1] + n*j - (m-j)*n+mod)%mod;
                sum+=dp[i][j];
            }
            sum %= mod;
        }

        sum = sum*MOD.getInv(2)%mod;
        sum = sum*MOD.nCkMod2(n*m-2, k-2)%mod;
        System.out.println(sum);
    }
}