# python 3.4.3
import sys
input = sys.stdin.readline

# -------------------------------------------------------------
# library
# -------------------------------------------------------------
class Combination:
    def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
    def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod

mod = 10**9+7
Combination = Combination(200010, mod)

# -------------------------------------------------------------
# main
# -------------------------------------------------------------

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

ans = 0
for d in range(1,N):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (N-d)*M*M
    t %= mod
    ans += t
    ans %= mod
for d in range(1,M):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (M-d)*N*N
    t %= mod
    ans += t
    ans %= mod

print(ans) import sys sys input = sys.stdin.readline input sys.stdin.readline sys.stdin sys stdin readline class Combination:
    def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
    def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod Combination def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
     __init__ self.mod = mod self.mod self mod mod self.fact = [1]*n self.fact self fact [1]*n [1] 1 n self.finv = [1]*n self.finv self finv [1]*n [1] 1 n self.inv  = [1]*n self.inv self inv [1]*n [1] 1 n for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
     i range(2,n) range 2 n self.fact[i] = (self.fact[i-1]*i) % self.mod self.fact[i] self.fact self fact i (self.fact[i-1]*i) % self.mod self.fact[i-1]*i self.fact[i-1] self.fact self fact i-1 i 1 i self.mod self mod self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod self.inv[i] self.inv self inv i self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod self.mod self mod self.inv[self.mod%i] * (self.mod//i)%self.mod self.inv[self.mod%i] * (self.mod//i) self.inv[self.mod%i] self.inv self inv self.mod%i self.mod self mod i self.mod//i self.mod self mod i self.mod self mod self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod self.finv[i] self.finv self finv i self.finv[i-1] * self.inv[i] % self.mod self.finv[i-1] * self.inv[i] self.finv[i-1] self.finv self finv i-1 i 1 self.inv[i] self.inv self inv i self.mod self mod self self n n mod mod def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod nCr if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod n<r n r return 0 0 return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) self.fact[n] self.fact self fact n self.finv[r] * self.finv[n-r] % self.mod self.finv[r] * self.finv[n-r] self.finv[r] self.finv self finv r self.finv[n-r] self.finv self finv n-r n r self.mod self mod self.mod self mod self self n n r r mod = 10**9+7 mod 10**9+7 10**9 10 9 7 Combination = Combination(200010, mod) Combination Combination(200010, mod) Combination 200010 mod N,M,K = map(int,input().split()) N map(int,input().split()) map int input().split() ().split () input split M K ans = 0 ans 0 for d in range(1,N):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (N-d)*M*M
    t %= mod
    ans += t
    ans %= mod d range(1,N) range 1 N t = d * Combination.nCr(N*M-2, K-2) t d * Combination.nCr(N*M-2, K-2) d Combination.nCr(N*M-2, K-2) Combination.nCr Combination nCr N*M-2 N*M N M 2 K-2 K 2 t %= mod t mod t *= (N-d)*M*M t (N-d)*M*M (N-d)*M N-d N d M M t %= mod t mod ans += t ans t ans %= mod ans mod for d in range(1,M):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (M-d)*N*N
    t %= mod
    ans += t
    ans %= mod d range(1,M) range 1 M t = d * Combination.nCr(N*M-2, K-2) t d * Combination.nCr(N*M-2, K-2) d Combination.nCr(N*M-2, K-2) Combination.nCr Combination nCr N*M-2 N*M N M 2 K-2 K 2 t %= mod t mod t *= (M-d)*N*N t (M-d)*N*N (M-d)*N M-d M d N N t %= mod t mod ans += t ans t ans %= mod ans mod print(ans) print ans K = map(int,input().split()) map(int,input().split()) K t = d * Combination.nCr(N*M-2, K-2) d * Combination.nCr(N*M-2, K-2) t N,M,K = map(int,input().split()) map(int,input().split()) N ans %= mod mod ans t *= (N-d)*M*M (N-d)*M*M t t %= mod mod t ans %= mod mod ans t *= (M-d)*N*N (M-d)*N*N t M,K = map(int,input().split()) map(int,input().split()) M class Combination:
    def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
    def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod class Combination:
    def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
    def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod Combination ans = 0 0 ans ans += t t ans t %= mod mod t input = sys.stdin.readline sys.stdin.readline input Combination = Combination(200010, mod) Combination(200010, mod) Combination t %= mod mod t mod = 10**9+7 10**9+7 mod t %= mod mod t ans += t t ans t = d * Combination.nCr(N*M-2, K-2) d * Combination.nCr(N*M-2, K-2) t
# python 3.4.3
import sys
input = sys.stdin.readline

# -------------------------------------------------------------
# library
# -------------------------------------------------------------
class Combination:
    def __init__(self, n, mod):
        self.mod = mod
        self.fact = [1]*n
        self.finv = [1]*n
        self.inv  = [1]*n
        for i in range(2,n):
            self.fact[i] = (self.fact[i-1]*i) % self.mod
            self.inv[i]  = self.mod - self.inv[self.mod%i] * (self.mod//i)%self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod
 
    def nCr(self, n, r):
        if n<r:
            return 0
        else:
            return self.fact[n] * (self.finv[r] * self.finv[n-r] % self.mod) % self.mod

mod = 10**9+7
Combination = Combination(200010, mod)

# -------------------------------------------------------------
# main
# -------------------------------------------------------------

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

ans = 0
for d in range(1,N):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (N-d)*M*M
    t %= mod
    ans += t
    ans %= mod
for d in range(1,M):
    t = d * Combination.nCr(N*M-2, K-2)
    t %= mod
    t *= (M-d)*N*N
    t %= mod
    ans += t
    ans %= mod

print(ans)
