For this Question: You are given a multiset of positive integers S. Initially, a number x is written on the blackboard. Now, you can perform the below operations zero or more times on blackboard numbers.

<ul><li>Choose any number written on the blackboard and then erase it from the blackboard. Suppose the chosen number is a. Now, choose some positive integer b and write two numbers, the quotient and remainder on dividing a by b on the blackboard.</li></ul>
For each x = 1, 2, 3 ... X, determine if it is possible to make the multiset of numbers written on blackboard equal to S after performing some operations, if the initial number is x.The first line contains a single integer T – the number of test cases.

The first line of each test case contains two space-separated integers – N (the size of multiset S) and X.

The second line contains N space-separated integers S<sub>1</sub>, S<sub>2</sub>, ... S<sub>N</sub>.

<b> Constraints: </b>
1 ≤ T ≤ 20
1 ≤ N ≤ 100
1 ≤ X ≤ 5×10<sup>5</sup>
1 ≤ S<sub>i</sub> ≤ 10<sup>9</sup>
Sum of X over all testcases doesn't exceed 5×10<sup>5</sup>.Print a string of length X whose i<sup>th</sup> character is '1' if it is possible to make the blackboard numbers equal to multiset S with i as the initial number on blackboard, and '0' otherwise.Sample Input 1:
1
2 5
1 1

Sample Output 1:
00111

Sample Explanation 1:
If x=4 is the only integer initially written on the blackboard, choose b=3 to have {1,1} as multiset of numbers on blackboard., I have written this Solution Code: #include<bits/stdc++.h>
using namespace std;

#define fix(f,n) std::fixed<<std::setprecision(n)<<f
#define epsi (double)(0.00000000001)
typedef long long int ll;
typedef unsigned long long int ull;
#define vi vector<ll>
#define pii pair<ll,ll>
#define vii vector<pii>
#define vvi vector<vi>
//#define max(a,b) ((a>b)?a:b)
//#define min(a,b) ((a>b)?b:a)
#define min3(a,b,c) min(min(a,b),c)
#define min4(a,b,c,d) min(min(a,b),min(c,d))
#define max3(a,b,c) max(max(a,b),c)
#define max4(a,b,c,d) max(max(a,b),max(c,d))
#define ff(a,b,c) for(int a=b; a<=c; a++)
#define frev(a,b,c) for(int a=c; a>=b; a--)
#define REP(a,b,c) for(int a=b; a<c; a++)
#define pb push_back
#define mp make_pair
#define endl "\n"
#define all(v) v.begin(),v.end()
#define sz(a) (ll)a.size()
#define F first
#define S second
#define ld long double
#define mem0(a) memset(a,0,sizeof(a))
#define mem1(a) memset(a,-1,sizeof(a))
#define ub upper_bound
#define lb lower_bound
#define setbits(x) __builtin_popcountll(x)
#define trav(a,x) for(auto &a:x)
#define make_unique(v) v.erase(unique(v.begin(), v.end()), v.end())
#define rev(arr) reverse(all(arr))
#define gcd(a,b) __gcd(a,b);
#define ub  upper_bound // '>'
#define lb  lower_bound // '>='
#define qi queue<ll>
#define fsh cout.flush()
#define si stack<ll>
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define fill(a,b) memset(a, b, sizeof(a))

template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}

const ll INF=1LL<<60;

void solve(){
	ll n,x;
    cin >> n >> x;
    vector<bool> ans(x+1,0);
    vi a(n);
    rep(i,0,n)cin>>a[i];
    ll mn=0;
    sort(all(a));
    rep(i,0,n){
        mn=mn*(1+a[i])+a[i];
        if(mn>x){
            rep(i,1,x+1) cout << ans[i];
            cout << endl;
            return;
        }
    }
    ans[mn]=1;
    vector<vector<pair<ll,ll>>> v(n,vector<pair<ll,ll>>(x+1,make_pair(INF,0)));
    vector<ll> dp(x+1,n);
    dp[mn]=0;
    rep(k,mn,x+1){
        rep(j,0,n){
            if(v[j][k%a[j]].first <= k){
                chmin(dp[k],v[j][k%a[j]].second);
            }
        }
        if(dp[k]==n)continue;
        rep(j,0,n){
            //if(i==j)continue;
            ll tmp=((mn-a[j])/(a[j]+1)+(k-mn));
            tmp=tmp*(a[j]+1)+a[j];
            chmin(v[j][tmp%a[j]],make_pair(tmp,dp[k]+1));
        }
    }
    rep(k,mn,x+1){
        if(dp[k]<n) ans[k]=1;
    }
    rep(i,1,x+1)cout<<ans[i];
    cout<<endl;
}

int main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	int t;
	cin >> t;
	while(t--){
		solve();
	}
}, In this Programming Language: C++, Now tell me if this Code is compilable or not?