J.cpp

#pragma GCC optimzize("Ofast,no-stack-protector")
#include<bits/stdc++.h>
//#define int long long
#define quick ios::sync_with_stdio(0);cin.tie(0);
#define rep(x,a,b) for(int x=a;x<=b;x++)
#define repd(x,a,b) for(int x=a;x>=b;x--)
#define lowbit(x) (x&-x)
#define sz(x) (int)(x.size())
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define mp make_pair
#define eb emplace_back
using namespace std;
typedef complex<int> P;
#define X real()
#define Y imag()
typedef pair<int,int> pii;
void debug(){
    cout<<"\n";
}
template <class T,class ... U >
void debug(T a, U ... b){
    cout<<a<<" ",debug(b...);
}
const int N=5e4+7;
const int INF=1e18;
bitset<N> A;
bitset<N> C[N];
int pref[N];
char a[N];
bool b[N];
bool ok[N];
void solve(){
    int n;
    cin>>n;
    unordered_map<int,int> pos;
    rep(i,1,n){
        cin>>a[i];
        pref[i]=pref[i-1];
        if(a[i]=='1') ++pref[i];
        else --pref[i];
    }
    rep(i,1,n){
        char bi;
        cin>>bi;
        b[i]=(bi-'0');
        ok[i]=true;
    }
    rep(i,1,n){
        int idx=pos[pref[i]];
        C[i]=(C[idx]<<(i-idx));
        A=(A<<1);
        if(a[i]=='1'){
            // increasing
            A|=(C[i-1]<<1);
        }
        else{
            //decreasing
            A^=C[i];
        }
        rep(k,1,n){
            if(i<=k){
                if(b[i]){
                    ok[k]&=(pref[i]>0);
                }
                else ok[k]&=(pref[i]<=0);
            }
            else{
                if(b[i]){
                    ok[k]&=(A[k]);
                }
                else{
                    ok[k]&=(~A[k]);
                }
            }
        }
        C[i][0]=true;
        pos[pref[i]]=i;
    }
    //rep(i,1,n) cout<<b[i];cout<<"\n";
    rep(k,1,n){
        cout<<ok[k];
    }cout<<"\n";

}
signed main(){
    quick
    int t;
    cin>>t;
    while(t--) solve();


    return 0;
}