Find all combinations of k-bit numbers with n bits set where 1 <= n <= k in sorted order

#include <bits/stdc++.h>
using namespace std;
# define K 16
vector<string>dp[K][K];

void fun(int k)
{
    string str="";
   
    
    for(int i=0;i<=k;i++)
    {
        dp[i][0].push_back(str);
        str+="0";
    }
    
   for(int i=1;i<=k;i++)
   {
       for(int j=1;j<=k;j++)
       {
           for(string str:dp[i-1][j])
               {
                   dp[i][j].push_back("0"+str);
               }
               
            for(string str: dp[i-1][j-1])
            {
                dp[i][j].push_back("1"+str);
            }
       }
   }
   
   for(int n=1;n<=k;n++)
   {
       for(string s:dp[k][n])
        cout<<s<<" ";
        
        
        cout<<endl;
   }
    
    

}

int main() {
	
	int k; cin>>k;
	fun(k);
	
	
	return 0;
}