Burning Midnight Oil

# 题目描述 有一天，Vasy被委托了一个非常重要的任务:在一个晚上写一个程序。该程序由n行代码组成。Vasya已经筋疲力尽了，所以他这样工作：首先他写v行代码，喝一杯茶，然后他写行代码，再喝一杯茶，然后他再写v行......以此类推。 ，表示a除以b后向下取整。若当前的值等于0，Vasya会睡着，但此之前他必须先完成程序。 Vasya想知道，在睡着之前，允许他写出不少于n行代码的最小值v可以取多少。 # 输入输出格式 ### 输入格式： 输入一行，n和k，由空格隔开。且1<=n<=10^9,2<=k<=10。 ### 输出格式： 输出一行：v。

One day a highly important task was commissioned to Vasya — writing a program in a night. The program consists of $ n $ lines of code. Vasya is already exhausted, so he works like that: first he writes $ v $ lines of code, drinks a cup of tea, then he writes as much as  lines, drinks another cup of tea, then he writes  lines and so on: , , , ... The expression  is regarded as the integral part from dividing number $ a $ by number $ b $ . The moment the current value  equals 0, Vasya immediately falls asleep and he wakes up only in the morning, when the program should already be finished. Vasya is wondering, what minimum allowable value $ v $ can take to let him write not less than $ n $ lines of code before he falls asleep.

The input consists of two integers $ n $ and $ k $ , separated by spaces — the size of the program in lines and the productivity reduction coefficient, $ 1<=n<=10^{9} $ , $ 2<=k<=10 $ .

Print the only integer — the minimum value of $ v $ that lets Vasya write the program in one night.

7 2

4

59 9

54

In the first sample the answer is $ v=4 $ . Vasya writes the code in the following portions: first $ 4 $ lines, then $ 2 $ , then $ 1 $ , and then Vasya falls asleep. Thus, he manages to write $ 4+2+1=7 $ lines in a night and complete the task. In the second sample the answer is $ v=54 $ . Vasya writes the code in the following portions: $ 54 $ , $ 6 $ . The total sum is $ 54+6=60 $ , that's even more than $ n=59 $ .