#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<random>
#include<array>
#include<assert.h>
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n'
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n'
#define DE(fmt,...) fprintf(stderr, "Line %d : " fmt "\n",__LINE__,##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pll>vpll;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
	r=0;bool w=0;char ch=getchar();
	while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
	while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
	return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
const int mod=998244353;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
int qpow(int x,int y){
	int s=1;
	while(y){
		if(y&1)s=1ll*s*x%mod;
		x=1ll*x*x%mod;
		y>>=1;
	}
	return s;
}
const int N=2000010;
int n,m,len;
int a[N],b[N],c[N];
char str[N];
int ans[N],A[N],B[N];
void solve(int t,int *f){
	int u=n,v=m;
	for(int i=1;i<=len;i++){
		int op=0;
		if(v==0)op=0;
		else if(u==0)op=1;
		else{
			if(!c[i])op=u<v?0:1;
			else op=u<v?1:0;
		}
		if(i<=t)op=1;
		if(op==0)a[u--]=c[i];
		else b[v--]=c[i];
	}
	for(int i=1;i<=n;i++)f[i]=a[i]+b[i];
	f[n+1]=0;
}
int check(){
	for(int i=n;i>=1;i--){
		if(A[i]!=B[i])
			return A[i]>B[i];
	}
	return 1;
}
void solve(){
	read(n,m);
	if(n<m)swap(n,m);
	len=n+m;
	for(int i=1;i<=len+2;i++)ans[i]=a[i]=b[i]=A[i]=B[i]=0;
	scanf("%s",str+1);
	for(int i=1;i<=len;i++)c[i]=str[i]-'0';
	vi vec;
	vec.pb(0);
	for(int i=1;i<=m;i++)if(c[i])vec.pb(i);
	int l=1,r=(int)vec.size()-1,mid,as=0;
	while(l<=r){
		mid=(l+r)>>1;
		solve(vec[mid],A);
		solve(vec[mid-1],B);
		if(check())as=mid,l=mid+1;
		else r=mid-1;
	}
	solve(vec[as],ans);
	for(int i=1;i<=n;i++){
		ans[i+1]+=ans[i]/2;
		ans[i]%=2;
	}
	if(ans[n+1])++n;
	while(n&&!ans[n])--n;
	if(n==0)puts("0");
	else{
		for(int i=n;i>=1;i--)cout<<ans[i];
		cout<<'\n';
	}
}
signed main(){
	int T;read(T);
	while(T--)solve();
    #ifdef do_while_true
//		cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
	#endif
	return 0;
}