#include<bits/stdc++.h>
using namespace std;
const long long mod=1e9+7;
long long fastpower(long long a,long long b){
	long long ans=1;
	while(b){
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
		b/=2;
	}
	return ans;
}
long long f[1000010];
void solve(){
	string s,t;
	int k;
	cin>>s>>t>>k;
	int n=max(t.size(),s.size());
	vector<int> a,b,c;
	for(int i=s.size()-1;i>=0;i--) a.push_back(s[i]-'0');
	for(int i=t.size()-1;i>=0;i--) b.push_back(t[i]-'0');
	for(int i=0;i<n;i++){
		if(i>=a.size()) a.push_back(0);
		if(i>=b.size()) b.push_back(0);
		c.push_back(a[i]^b[i]);
	}
	int cnt=0;
	for(int i=0;i<c.size();i+=2){
		if(i+1==c.size()) c.push_back(0);
		if(c[i]==0&&c[i+1]==0) cnt=i+1;
		else break;
	}
	if(cnt==c.size()/2){
		cout<<(f[k-1]-1+mod)%mod<<endl;
		return ;
	}
	if(k-1>cnt) {
		cout<<-1<<endl;
		return ;
	}
	long long ans=0;
	long long inv3=fastpower(3,mod-2);
	ans=(fastpower(4,k)-4)*inv3%mod;
	for(int i=0;i<c.size();i+=2){
		if(i+1==c.size()) c.push_back(0);
		if(c[i]==1&&c[i+1]==0){
			ans=(ans+1*f[i/2]%mod)%mod;
		}
		if(c[i]==1&&c[i+1]==1){
			ans=(ans+2*f[i/2]%mod)%mod;
		}
		if(c[i]==0&&c[i+1]==1){
			ans=(ans+3*f[i/2]%mod)%mod;
		}
	}
	cout<<ans<<endl;
}
int main(){
	f[0]=1;
	for(int i=1;i<=1000000;i++){
		f[i]=(f[i-1]*4%mod+1)%mod;
	}
	int t;
	cin>>t;
	while(t--){
		solve();
	}
	return 0;
}