#include<bits/stdc++.h>
using namespace std;
constexpr int N=1000005;
constexpr int MOD=1000000007;
int qpow(int a,int b)
{
    int res=1;
    while(b)
    {
        if(b&1) res=(long long)res*a%MOD;
        a=(long long)a*a%MOD,b>>=1;
    }
    return res;
}
int getinv(int x)
{
    return qpow(x,MOD-2);
}
string a,b;
int k;
void solve()
{
    cin>>a>>b>>k;
    reverse(a.begin(),a.end());
    reverse(b.begin(),b.end());
    string s=a;
    while(s.size()<b.size()) s+='0';
    for(int i=0;i<(int)s.size();i++)
        if(i<(int)b.size()&&b[i]=='1') s[i]=s[i]=='0'?'1':'0';
    while((int)s.size()>1&&s.back()=='0') s.pop_back();
    if(s=="0")
    {
        int ans=(long long)(qpow(4,k)-4+MOD)*getinv(3)%MOD;
        cout<<ans<<"\n";
        return;
    }
    int cnt=0;
    for(int i=0;i+1<(int)s.size();i+=2)
        if(s[i]=='0'&&s[i+1]=='0') cnt++;
    if(cnt<k-1)
    {
        cout<<-1<<"\n";
        return;
    }
    if(s.size()%2==1) s+='0';
    int pw=1;
    int ans=0;
    for(int i=0;i+1<(int)s.size();i+=2)
    {
        int c=0;
        if(s[i]=='1'&&s[i+1]=='0') c=1;
        else if(s[i]=='1'&&s[i+1]=='1') c=2;
        else if(s[i]=='0'&&s[i+1]=='1') c=3;
        int val=(long long)(qpow(4,i/2+1)-1+MOD)*getinv(3)%MOD;
        ans=(ans+(long long)c*val)%MOD;
    }
    ans=(ans+(long long)(qpow(4,k)-4+MOD)*getinv(3))%MOD;
    cout<<ans<<"\n";
    return; 
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr),cout.tie(nullptr);
    int T;
    cin>>T;
    while(T--)
        solve(); 
    return 0;
}