#include<bits/stdc++.h>
#define ing long long 
typedef long long ll;
using namespace std;
const int N=2e3+10,M=1e6+10,mod=1e9+7;

ll power(ll a,ll b){
	ll ans=1;
	for(;b;b>>=1){
		if(b&1)ans=ans*a%mod;
		a=a*a%mod;
	}
	return ans;
}

ll n,m,K;
ll A[N][N],f[M],incf[M];
void init(int len){
	f[0]=1;
	for(int i=1;i<=len;i++)f[i]=f[i-1]*i%mod;
	incf[len]=power(f[len],mod-2);
	for(int i=len-1;i>=0;i--)incf[i]=incf[i+1]*(i+1)%mod;
}

ll C(ll a,ll b){
	if(a<b)return 0;
	return f[a]*incf[b]%mod*incf[a-b]%mod;
}

ll Guess(){
	ll op=1,ans=1;
	for(int i=1;i<=K;i++){
		int pos=i;
		for(int j=i+1;j<=K;j++)
			if(A[j][i]>A[pos][i])pos=j;
		if(i!=pos)op=-op,swap(A[i],A[pos]);
		if(!A[i][i])return 0;
		for(int j=1;j<=K;j++){
			if(j==i)continue;
			ll tmp=A[j][i]*power(A[i][i],mod-2)%mod;
			for(int k=1;k<=K;k++)
				A[j][k]=(A[j][k]-tmp*A[i][k]%mod+mod)%mod;
		}
		ans=ans*A[i][i]%mod;
		ll tmp=power(A[i][i],mod-2);
		for(int j=1;j<=K;j++)A[i][j]=A[i][j]*tmp%mod;
	}
	return (ans*op%mod+mod)%mod;
}

signed main(){
	init(M-1);
	scanf("%lld%lld%lld",&n,&m,&K);
	for(int i=1;i<=K;i++)
		for(int j=1;j<=K;j++){
			ll x=n+(j-i),y=m-(j-i);
			A[i][j]=C(x+y,x);
		}
	printf("%lld\n",Guess());
	return 0;
}