import sys
input = sys.stdin.readline
import copy

def main():
    N,M,K = map(int,input().split())
    MOD = 10**9+7
    fac = [0 for _ in range(N*M-1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

    xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD
    ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD
    print((xa+ya)*coef(N*M-2,K-2)%MOD)

if __name__ == "__main__":
    main() import sys sys input = sys.stdin.readline input sys.stdin.readline sys.stdin sys stdin readline import copy copy def main():
    N,M,K = map(int,input().split())
    MOD = 10**9+7
    fac = [0 for _ in range(N*M-1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

    xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD
    ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD
    print((xa+ya)*coef(N*M-2,K-2)%MOD) main N,M,K = map(int,input().split()) N map(int,input().split()) map int input().split() ().split () input split M K MOD = 10**9+7 MOD 10**9+7 10**9 10 9 7 0 for _ in range(N*M-1) for _ in range(N*M-1) _ range(N*M-1) range N*M-1 N*M N M 1 for _ in range(N*M-1) 0 fac = [0 for _ in range(N*M-1)] fac [0 for _ in range(N*M-1)] fac[0],fac[1] = 1,1 fac[0] fac 0 1 fac[1] fac 1 1 inv = copy.deepcopy(fac) inv copy.deepcopy(fac) copy.deepcopy copy deepcopy fac invfac = copy.deepcopy(fac) invfac copy.deepcopy(fac) copy.deepcopy copy deepcopy fac for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
     i range(2,N*M-1) range 2 N*M-1 N*M N M 1 fac[i] = (fac[i-1]*i)%MOD fac[i] fac i (fac[i-1]*i)%MOD fac[i-1]*i fac[i-1] fac i-1 i 1 i MOD inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD inv[i] inv i MOD-(MOD//i)*inv[MOD%i]%MOD MOD (MOD//i)*inv[MOD%i]%MOD (MOD//i)*inv[MOD%i] MOD//i MOD i inv[MOD%i] inv MOD%i MOD i MOD invfac[i] = (invfac[i-1]*inv[i])%MOD invfac[i] invfac i (invfac[i-1]*inv[i])%MOD invfac[i-1]*inv[i] invfac[i-1] invfac i-1 i 1 inv[i] inv i MOD def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

     coef num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD) num ((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD ((fac[x]*invfac[y])%MOD)*invfac[x-y] (fac[x]*invfac[y])%MOD fac[x]*invfac[y] fac[x] fac x invfac[y] invfac y MOD invfac[x-y] invfac x-y x y MOD return num num x x y y xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD xa ((M**2)*N*(N-1)*(N+1)//6)%MOD (M**2)*N*(N-1)*(N+1)//6 (M**2)*N*(N-1)*(N+1) (M**2)*N*(N-1) (M**2)*N M**2 M 2 N N-1 N 1 N+1 N 1 6 MOD ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD ya ((N**2)*M*(M-1)*(M+1)//6)%MOD (N**2)*M*(M-1)*(M+1)//6 (N**2)*M*(M-1)*(M+1) (N**2)*M*(M-1) (N**2)*M N**2 N 2 M M-1 M 1 M+1 M 1 6 MOD print((xa+ya)*coef(N*M-2,K-2)%MOD) print (xa+ya)*coef(N*M-2,K-2)%MOD (xa+ya)*coef(N*M-2,K-2) xa+ya xa ya coef(N*M-2,K-2) coef N*M-2 N*M N M 2 K-2 K 2 MOD if __name__ == "__main__":
    main() __name__ == "__main__" __name__ "__main__" main() main def main():
    N,M,K = map(int,input().split())
    MOD = 10**9+7
    fac = [0 for _ in range(N*M-1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

    xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD
    ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD
    print((xa+ya)*coef(N*M-2,K-2)%MOD) def main():
    N,M,K = map(int,input().split())
    MOD = 10**9+7
    fac = [0 for _ in range(N*M-1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

    xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD
    ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD
    print((xa+ya)*coef(N*M-2,K-2)%MOD) main input = sys.stdin.readline sys.stdin.readline input
import sys
input = sys.stdin.readline
import copy

def main():
    N,M,K = map(int,input().split())
    MOD = 10**9+7
    fac = [0 for _ in range(N*M-1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,N*M-1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD)
        return num

    xa = ((M**2)*N*(N-1)*(N+1)//6)%MOD
    ya = ((N**2)*M*(M-1)*(M+1)//6)%MOD
    print((xa+ya)*coef(N*M-2,K-2)%MOD)

if __name__ == "__main__":
    main()
