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.

#include<iostream>

#include<cmath>

using namespace std;

#define ll long long

int main()

{

    ll m,q,ans=,i,t;

    cin>>m>>q;

    ll sum = ;

    while(){

        if(pow(,ans)>m)

            break;

        t=ans*q+m/(pow(,ans));

        int num = m/pow(,ans);

        if(m-pow(,ans)*num!=)

            t++;

        sum = min(t,sum);

        ans++;

    }

    cout<<sum<<endl;

}