CF 379A New Year Candles

Vasily the Programmer loves romance, so this year he decided to illuminate his room with candles.

Vasily has a candles.When Vasily lights up a new candle, it first burns for an hour and then it goes out. Vasily is smart, so he can make bwent out candles into a new candle. As a result, this new candle can be used like any other new candle.

Now Vasily wonders: for how many hours can his candles light up the room if he acts optimally well? Help him find this number.

Input

The single line contains two integers, a and b (1 ≤ a ≤ 1000; 2 ≤ b ≤ 1000).

Output

Print a single integer — the number of hours Vasily can light up the room for.

Examples

input

4 2

output

7

input

6 3

output

8

Note

Consider the first sample. For the first four hours Vasily lights up new candles, then he uses four burned out candles to make two new ones and lights them up. When these candles go out (stop burning), Vasily can make another candle. Overall, Vasily can light up the room for 7 hours.

题目大意*（一开始我是读不懂的） ： 有n个蜡烛， 燃烧完会产生n个蜡烛头， 但是m个蜡烛头又能组合为一个新的蜡烛 ； 问最多可以烧几根蜡烛；

样例：4根全部燃烧， 2个可以组成一根； 所以最初4根， 4个蜡烛头可以组成2个蜡烛，后又可以组成1个蜡烛。1个蜡烛头不能组成蜡烛， 结束；

  所以为4+2+1 = 7 ；

AC代码：

#include <bits/stdc++.h>using namespace std ;int main(){    int n , m , p ;    cin>>n>>m;    int ans = n ;    while(n>=m)    {        ans+=n/m;        n = n%m + n/m ;    }    cout<<ans<<endl;    return 0 ;}