If $$$n=1$$$, There is only one possible $$$\it{Lucky \ array}$$$. It is guaranteed that the given array is $$$\it{Lucky \ array}$$$ so there is no other $$$\it{Lucky \ array}$$$ to output. Hence the answer is $$$-1$$$.

For $$$n>1$$$, it is easy to see that there are more than one possible $$$\it{Lucky \ array}$$$. So we can use the following pattern to construct the $$$\it{Lucky \ array}$$$ :

$$$ 0 \ 1 \ 0 \ 1 \ 0 \ 1 \ ....$$$

If this constructed array is equal to the given array then we can swap the elements in $$$2^{nd}$$$ and $$$3^{rd}$$$ positions if $$$n>2$$$, otherwise we can just set the $$$2^{nd}$$$ to $$$0$$$.

Note that there are many possible constructions, the above mentioned is one of them

Time Complexity : $$$O(n)$$$.

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fast                       \
 ios_base::sync_with_stdio(0);      \
 cin.tie(0);                         \
 cout.tie(0);

int main(){
    fast;
    ll t;
    cin>>t;
    while(t--){
        int n;
        cin>>n;
        vector<int> a(n);
        for(int i=0;i<n;i++) cin>>a[i];
        if(n==1) cout<<"-1\n";
        else if(n==2){
            if(a[1]==1) cout<<"0 0\n";
            else cout<<"0 1\n";
        }
        else{
            vector<int> b(n,0);
            for(int i=1;i<n;i+=2) b[i]=1;
            if(a==b) swap(b[1],b[2]);
            for(auto i:b) cout<<i<<" ";
            cout<<"\n";
        }
    }
}

Coming soon...

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fast                       \
 ios_base::sync_with_stdio(0);      \
 cin.tie(0);                         \
 cout.tie(0);

int main(){
    fast;
    ll t;
    cin>>t;
    while(t--){
        ll n,a,b;
        cin>>n>>a>>b;
        vector<ll> v(n);
        for(ll i=0;i<n;i++) cin>>v[i];
        ll l=0,r=1e9,ans=1e9;
        while(l<=r){
            ll m=(l+r)/2;
            ll ops=0;
            for(ll i=0;i<n;i++){
                if(v[i]>b*m){
                    ops+=((v[i]-b*m+(a-b-1))/(a-b));
                }
            }
            if(ops<=m){
                ans=m;
                r=m-1;
            }
            else l=m+1;
        }
        cout<<ans<<"\n";
    }
}

Coming soon...

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fast                       \
 ios_base::sync_with_stdio(0);      \
 cin.tie(0);                         \
 cout.tie(0);

int main(){
    fast;
    ll t;
    cin>>t;
    while(t--){
        ll n;
        cin>>n;
        vector<ll> a(n);
        for(ll i=0;i<n;i++) cin>>a[i];
        ll ans=0,val=1;
        for(ll i=0;i<n;i++){
            ll res=(a[i]-1)/val;
            if(res>0){
                ans+=res;
                a[i]=1;
            }
            if(val==a[i]) val++;
        }
        ans++;
        cout<<ans<<"\n";
    }
}

Coming soon...

#include <map>
#include <set>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <bitset>
using namespace std;
typedef double db; 
typedef long long ll;
typedef unsigned long long ull;
const int N=1000010;
const int LOGN=28;
const ll  TMD=0;
const ll  INF=2147483647;
int T;
ll  n,m;
int tag[N];

int main()
{
	//freopen("test.in","r",stdin);
	
	scanf("%d",&T);
	while(T--)
	{
		scanf("%I64d%I64d",&n,&m);
		ll mx=n*(n+1)/2-2,mn=-mx,sum=mn,cur1,cur2;
		vector<ll> v[2];
		if(m<mn||m>mx||((mx&1)^(m&1)))
		{
			printf("NO\n");
			continue;
		}
		printf("YES\n");
		tag[1]=1;
		for(int i=2;i<=n;i++) tag[i]=0;
		for(int i=2;i<=n;i++)
		{
			tag[i]=1;
			sum+=2*i;
			if(sum>=m)
			{
				tag[(sum-m)/2]=0;
				break;
			}
		}
		for(int i=1;i<=n;i++) v[tag[i]].push_back(i);
		cur1=v[1][0];
		for(int i=1;i<v[0].size();i++) 
		{
			printf("%I64d %I64d\n",cur1,v[0][i]);
			cur1-=v[0][i];
		}
		cur2=v[0][0];
		for(int i=1;i<v[1].size();i++) 
		{
			printf("%I64d %I64d\n",cur2,v[1][i]);
			cur2-=v[1][i];
		}
		printf("%I64d %I64d\n",cur1,cur2);
	}
	
	//fclose(stdin);
	return 0;
}

Coming soon...

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fast                       \
 ios_base::sync_with_stdio(0);      \
 cin.tie(0);                         \
 cout.tie(0);
 
int n;
vector<int> v1;
 
int query(vector<int> v){
    cout<<"? ";
    for(int i=0;i<(int)v.size();i++) cout<<v[i]+1<<" ";
    cout<<endl;
    int x;
    cin>>x;
    if(x>(n/2)) return 1;
    return 0;
}
 
int sol(int j){
    vector<int> v(n/2);
    for(int i=0;i<n/2;i++) v[i]=v1[i+j];
    return query(v);
}
 
int main(){
    fast;
    ll t;
    cin>>t;
    while(t--){
        cin>>n;
        v1.clear();
        v1.resize(n);
        for(int i=0;i<n;i++) v1[i]=i;
        int l=0,r=n/2;
        int vl=sol(0),vr=sol(n/2);
        while(l+1<r){
            int m=(l+r)/2;
            int vm=sol(m);
            if(vm==vl) l=m;
            else r=m;
        }
        vector<int> v2,v3;
        for(int i=r;i<(r+(n/2)-1);i++){
            v2.push_back(v1[i]);
            v3.push_back(v1[(i+(n/2))%n]);
        }
        vector<int> ans(n);
        ans[v1[l]]=vl;
        ans[v1[l+(n/2)]]=vr;
        for(int i=0;i<(int)v2.size();i++){
            vector<int> v=v3;
            v.push_back(v2[i]);
            ans[v2[i]]=query(v);
        }
        for(int i=0;i<(int)v3.size();i++){
            vector<int> v=v2;
            v.push_back(v3[i]);
            ans[v3[i]]=query(v);
        }
        vector<int> even,odd;
        for(int i=0;i<n;i++){
            if(ans[i]==0) even.push_back(i+1);
            else odd.push_back(i+1);
        }
        cout<<"! ";
        for(int i=0;i<(int)even.size();i++){
            cout<<even[i]<<" ";
            cout<<odd[i]<<" ";
        }
        cout<<endl;
    }
}

Coming soon...

~~~~~

~~~~~