import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def modfact(n):
    fact=[1]*(n+1)
    invfact=[1]*(n+1)
    for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
    invfact[n]=pow(fact[n],MOD-2,MOD)
    for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
    return fact,invfact

def resolve():
    n,m,k=map(int,input().split())
    fact,invfact=modfact(n*m-2)
    ans=1
    ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k]
    ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6
    print(ans%MOD)
resolve() import sys sys sys.setrecursionlimit(2147483647) sys.setrecursionlimit sys setrecursionlimit 2147483647 INF=float("inf") INF float("inf") float "inf" MOD=10**9+7 MOD 10**9+7 10**9 10 9 7 input=lambda :sys.stdin.readline().rstrip() input lambda :sys.stdin.readline().rstrip() sys.stdin.readline().rstrip() sys.stdin.readline().rstrip sys.stdin.readline() sys.stdin.readline sys.stdin sys stdin readline rstrip def modfact(n):
    fact=[1]*(n+1)
    invfact=[1]*(n+1)
    for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
    invfact[n]=pow(fact[n],MOD-2,MOD)
    for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
    return fact,invfact modfact fact=[1]*(n+1) fact [1]*(n+1) [1] 1 n+1 n 1 invfact=[1]*(n+1) invfact [1]*(n+1) [1] 1 n+1 n 1 for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
     i range(1,n+1) range 1 n+1 n 1 fact[i]=i*fact[i-1]%MOD fact[i] fact i i*fact[i-1]%MOD i*fact[i-1] i fact[i-1] fact i-1 i 1 MOD invfact[n]=pow(fact[n],MOD-2,MOD) invfact[n] invfact n pow(fact[n],MOD-2,MOD) pow fact[n] fact n MOD-2 MOD 2 MOD for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
     i range(n-1,-1,-1) range n-1 n 1 -1 -1 invfact[i]=invfact[i+1]*(i+1)%MOD invfact[i] invfact i invfact[i+1]*(i+1)%MOD invfact[i+1]*(i+1) invfact[i+1] invfact i+1 i 1 i+1 i 1 MOD return fact,invfact return fact,invfact fact invfact n n def resolve():
    n,m,k=map(int,input().split())
    fact,invfact=modfact(n*m-2)
    ans=1
    ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k]
    ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6
    print(ans%MOD) resolve n,m,k=map(int,input().split()) n map(int,input().split()) map int input().split() ().split () input split m k fact,invfact=modfact(n*m-2) fact modfact(n*m-2) modfact n*m-2 n*m n m 2 invfact ans=1 ans 1 ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k] ans fact[m*n-2]*invfact[k-2]*invfact[m*n-k] fact[m*n-2]*invfact[k-2] fact[m*n-2] fact m*n-2 m*n m n 2 invfact[k-2] invfact k-2 k 2 invfact[m*n-k] invfact m*n-k m*n m n k ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6 ans ((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6 (n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n (n-1)*n*(n+1)*m*m (n-1)*n*(n+1)*m (n-1)*n*(n+1) (n-1)*n n-1 n 1 n n+1 n 1 m m (m-1)*m*(m+1)*n*n (m-1)*m*(m+1)*n (m-1)*m*(m+1) (m-1)*m m-1 m 1 m m+1 m 1 n n 6 print(ans%MOD) print ans%MOD ans MOD resolve() resolve INF=float("inf") float("inf") INF input=lambda :sys.stdin.readline().rstrip() lambda :sys.stdin.readline().rstrip() input def modfact(n):
    fact=[1]*(n+1)
    invfact=[1]*(n+1)
    for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
    invfact[n]=pow(fact[n],MOD-2,MOD)
    for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
    return fact,invfact def modfact(n):
    fact=[1]*(n+1)
    invfact=[1]*(n+1)
    for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
    invfact[n]=pow(fact[n],MOD-2,MOD)
    for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
    return fact,invfact modfact def resolve():
    n,m,k=map(int,input().split())
    fact,invfact=modfact(n*m-2)
    ans=1
    ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k]
    ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6
    print(ans%MOD) def resolve():
    n,m,k=map(int,input().split())
    fact,invfact=modfact(n*m-2)
    ans=1
    ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k]
    ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6
    print(ans%MOD) resolve MOD=10**9+7 10**9+7 MOD
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def modfact(n):
    fact=[1]*(n+1)
    invfact=[1]*(n+1)
    for i in range(1,n+1):
        fact[i]=i*fact[i-1]%MOD
    invfact[n]=pow(fact[n],MOD-2,MOD)
    for i in range(n-1,-1,-1):
        invfact[i]=invfact[i+1]*(i+1)%MOD
    return fact,invfact

def resolve():
    n,m,k=map(int,input().split())
    fact,invfact=modfact(n*m-2)
    ans=1
    ans*=fact[m*n-2]*invfact[k-2]*invfact[m*n-k]
    ans*=((n-1)*n*(n+1)*m*m+(m-1)*m*(m+1)*n*n)//6
    print(ans%MOD)
resolve()