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There are N jobs to be finished. It takes a robot 1 hour to finish one job.

At the beginning you have only one robot. Luckily a robot may build more robots identical to itself. It takes a robot Q hours to build another robot.  

So what is the minimum number of hours to finish N jobs?

Note two or more robots working on the same job or building the same robot won't accelerate the progress.

 

Input

The first line contains 2 integers, N and Q.  

For 70% of the data, 1 <= N <= 1000000  

For 100% of the data, 1 <= N <= 1000000000000, 1 <= Q <= 1000

 

Output

The minimum number of hours.

Sample Input

10 1

Sample Output

5

#include <iostream>

using namespace std;

int main()
{   long long n,m,t,k,ans;
     cin>>n>>m;
     t=2,k=1;
     ans=n;
     while(t<n){
        ans=min(ans,k*m+n/t+(n%t==0?0:1));
        t=t*2;
        k++;
     }
     cout<<ans<<endl;
    return 0;
}