class Factorial():
    def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
    def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod

from collections import deque

MOD = 1000000007

N,M,K = map(int,input().split())

F = Factorial(N*M,MOD)

print(F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1)//6%MOD) class Factorial():
    def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
    def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod Factorial def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
     __init__ self.mod = mod self.mod self mod mod 0 for _ in range(n+1) for _ in range(n+1) _ range(n+1) range n+1 n 1 for _ in range(n+1) 0 self.factorial = [0 for _ in range(n+1)] self.factorial self factorial [0 for _ in range(n+1)] 0 for _ in range(n+1) for _ in range(n+1) _ range(n+1) range n+1 n 1 for _ in range(n+1) 0 self.inv = [0 for _ in range(n+1)] self.inv self inv [0 for _ in range(n+1)] self.factorial[0] = 1 self.factorial[0] self.factorial self factorial 0 1 self.inv[0] = 1 self.inv[0] self.inv self inv 0 1 for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
         i range(n) range n self.factorial[i+1] = self.factorial[i]*(i+1)%mod self.factorial[i+1] self.factorial self factorial i+1 i 1 self.factorial[i]*(i+1)%mod self.factorial[i]*(i+1) self.factorial[i] self.factorial self factorial i i+1 i 1 mod self.inv[n] = pow(self.factorial[n],mod-2,mod) self.inv[n] self.inv self inv n pow(self.factorial[n],mod-2,mod) pow self.factorial[n] self.factorial self factorial n mod-2 mod 2 mod for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
     i range(n)[::-1] (n) range n ::-1 -1 self.inv[i] = self.inv[i+1]*(i+1)%mod self.inv[i] self.inv self inv i self.inv[i+1]*(i+1)%mod self.inv[i+1]*(i+1) self.inv[i+1] self.inv self inv i+1 i 1 i+1 i 1 mod self self n n mod mod def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod comb return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod self.factorial[m]*self.inv[k]*self.inv[m-k] self.factorial[m]*self.inv[k] self.factorial[m] self.factorial self factorial m self.inv[k] self.inv self inv k self.inv[m-k] self.inv self inv m-k m k self.mod self mod self self m m k k from collections import deque MOD = 1000000007 MOD 1000000007 N,M,K = map(int,input().split()) N map(int,input().split()) map int input().split() ().split () input split M K F = Factorial(N*M,MOD) F Factorial(N*M,MOD) Factorial N*M N M MOD print(F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1)//6%MOD) print F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1)//6%MOD F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1)//6 F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1) F.comb(N*M-2,K-2)*(N+M)*N*M F.comb(N*M-2,K-2)*(N+M)*N F.comb(N*M-2,K-2)*(N+M) F.comb(N*M-2,K-2) F.comb F comb N*M-2 N*M N M 2 K-2 K 2 N+M N M N M N*M-1 N*M N M 1 6 MOD M,K = map(int,input().split()) map(int,input().split()) M K = map(int,input().split()) map(int,input().split()) K MOD = 1000000007 1000000007 MOD N,M,K = map(int,input().split()) map(int,input().split()) N class Factorial():
    def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
    def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod class Factorial():
    def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
    def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod Factorial F = Factorial(N*M,MOD) Factorial(N*M,MOD) F
class Factorial():
    def __init__(self,n,mod):
        self.mod = mod
        self.factorial = [0 for _ in range(n+1)]
        self.inv = [0 for _ in range(n+1)]
        self.factorial[0] = 1
        self.inv[0] = 1
        for i in range(n):
            self.factorial[i+1] = self.factorial[i]*(i+1)%mod
        self.inv[n] = pow(self.factorial[n],mod-2,mod)
        for i in range(n)[::-1]:
            self.inv[i] = self.inv[i+1]*(i+1)%mod
    def comb(self,m,k): #組み合わせ 0<=k<=m<=n 重複組み合わせはcomb(m+k-1,k)
        return self.factorial[m]*self.inv[k]*self.inv[m-k]%self.mod

from collections import deque

MOD = 1000000007

N,M,K = map(int,input().split())

F = Factorial(N*M,MOD)

print(F.comb(N*M-2,K-2)*(N+M)*N*M*(N*M-1)//6%MOD)