寒假训练5-c

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 b went 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.
问题简述：共有a支蜡烛，每有b支蜡烛可以制作成一支新的蜡烛，问共有多少支蜡烛。
问题分析：分3种情况考虑，a>b的情况注意循环的判断条件。