MOD = 10**9 + 7

def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn

def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u

def MOD_COM2(n, r):
    return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD

def main():
    n, m, k = map(int, input().split())
    comb = MOD_COM2(n*m-2, k-2)
    ans = 0
    for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
    for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
    print(ans%MOD)

if __name__ == "__main__":
    main() MOD = 10**9 + 7 MOD 10**9 + 7 10**9 10 9 7 def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn MOD_perm rtn = 1 rtn 1 for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
     _ range(r) range r rtn *= n rtn n rtn %= MOD rtn MOD n -= 1 n 1 return rtn rtn n n r r def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u MOD_inv b = MOD b MOD u = 1 u 1 v = 0 v 0 while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
     b > 0 b 0 t = a // b t a // b a b a -= t * b a t * b t b a, b = b, a a b b a u -= t * v u t * v t v u, v = v, u u v v u u = u % MOD u u % MOD u MOD if u < 0:
        u += MOD
     u < 0 u 0 u += MOD u MOD return u u a a def MOD_COM2(n, r):
    return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD MOD_COM2 return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) MOD_perm(n, r) MOD_perm n r MOD_inv(MOD_perm(r, r)) MOD_inv MOD_perm(r, r) MOD_perm r r MOD n n r r def main():
    n, m, k = map(int, input().split())
    comb = MOD_COM2(n*m-2, k-2)
    ans = 0
    for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
    for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
    print(ans%MOD) main n, m, k = map(int, input().split()) n map(int, input().split()) map int input().split() ().split () input split m k comb = MOD_COM2(n*m-2, k-2) comb MOD_COM2(n*m-2, k-2) MOD_COM2 n*m-2 n*m n m 2 k-2 k 2 ans = 0 ans 0 for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
     i range(1, n+1) range 1 n+1 n 1 U = (i-1)*i//2 U (i-1)*i//2 (i-1)*i i-1 i 1 i 2 U *= m*m U m*m m m U *= comb U comb U %= MOD U MOD ans += U ans U ans %= MOD ans MOD for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
     j range(1, m+1) range 1 m+1 m 1 L = (j-1)*j//2 L (j-1)*j//2 (j-1)*j j-1 j 1 j 2 L *= n*n L n*n n n L *= comb L comb L %= MOD L MOD ans += L ans L ans %= MOD ans MOD print(ans%MOD) print ans%MOD ans MOD if __name__ == "__main__":
    main() __name__ == "__main__" __name__ "__main__" main() main def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u MOD_inv MOD = 10**9 + 7 10**9 + 7 MOD def main():
    n, m, k = map(int, input().split())
    comb = MOD_COM2(n*m-2, k-2)
    ans = 0
    for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
    for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
    print(ans%MOD) def main():
    n, m, k = map(int, input().split())
    comb = MOD_COM2(n*m-2, k-2)
    ans = 0
    for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
    for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
    print(ans%MOD) main def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn MOD_perm def MOD_COM2(n, r):
    return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD def MOD_COM2(n, r):
    return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD MOD_COM2
MOD = 10**9 + 7

def MOD_perm(n, r):
    rtn = 1
    for _ in range(r):
        rtn *= n
        rtn %= MOD
        n -= 1
    return rtn

def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u

def MOD_COM2(n, r):
    return MOD_perm(n, r) * MOD_inv(MOD_perm(r, r)) % MOD

def main():
    n, m, k = map(int, input().split())
    comb = MOD_COM2(n*m-2, k-2)
    ans = 0
    for i in range(1, n+1):
        U = (i-1)*i//2
        U *= m*m
        U *= comb
        U %= MOD
        ans += U
        ans %= MOD
    for j in range(1, m+1):
        L = (j-1)*j//2
        L *= n*n
        L *= comb
        L %= MOD
        ans += L
        ans %= MOD
    print(ans%MOD)

if __name__ == "__main__":
    main()