CF165B.Burning Midnight Oil

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.

一天，瓦西娅接到一项极其重要的任务——在夜间编写一个程序。该程序共包含 $n$ 行代码。此时瓦西娅已精疲力竭，因此他采用如下方式工作：首先编写 $v$ 行代码，然后喝一杯茶；接着编写 $\left\lfloor \frac{v}{2} \right\rfloor$ 行代码，再喝一杯茶；接着编写 $\left\lfloor \frac{v}{4} \right\rfloor$ 行代码，依此类推：$\left\lfloor \frac{v}{8} \right\rfloor$，$\left\lfloor \frac{v}{16} \right\rfloor$，$\left\lfloor \frac{v}{32} \right\rfloor$，……

其中，表达式 $\left\lfloor \frac{a}{b} \right\rfloor$ 表示将整数 $a$ 除以整数 $b$ 后所得的向下取整（即整数部分）。

一旦当前值 $\left\lfloor \frac{v}{2^k} \right\rfloor$ 等于 $0$，瓦西娅会立刻睡着，并一直睡到第二天早晨——而那时程序本应早已完成。

瓦西娅想知道：为使他在睡着前能至少写出 $n$ 行代码，$v$ 的最小可能取值是多少？

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 ≤ 109, 2 ≤ k ≤ 10.

输入包含两个整数 $n$ 和 $k$，以空格分隔——分别表示程序的行数和生产率降低系数，满足 $1 \leq n \leq 10^9$，$2 \leq k \leq 10$。

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

输出唯一的整数——使得瓦西娅能在一夜之间编写完该程序的最小 v 值。

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.

在第一个样例中，答案为 $v = 4$。瓦夏按以下段落编写代码：先写 4 行，然后写 2 行，再写 1 行，之后瓦夏便睡着了。因此，他一晚上共编写了 $4 + 2 + 1 = 7$ 行代码，并完成了任务。

在第二个样例中，答案为 $v = 54$。瓦夏按以下段落编写代码：54 行、6 行。总和为 $54 + 6 = 60$，甚至超过了 $n = 59$。