Help me in solving ZOOZ problem

help
,
1

My issue

My code

#include <iostream>
#include<bitset>
#include<math.h>
using namespace std;

string toBinary(int n)
{
    string r;
    while(n!=0) {r=(n%2==0 ?"0":"1")+r; n/=2;}
    return r;
}
int main() {
	// your code goes here
	int t;
	cin>>t;
	while(t--)
	{
	  int n;
	  string ans;
	  cin>>n;
	 int i = pow(2,n-1)+1;
	    
	   
	      ans = toBinary(i);
	      cout<<ans<<endl;
	    
	   
	}
	return 0;
}

Where is the error in my code?
Problem Link: ZOOZ Problem - CodeChef

2

@tvj414
your logic is not right
logic is quite simple first print 01 then print n-2 times 0