Burning Midnight Oil

2000ms

262144K

Description:

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 $\text{[math]}$ lines, drinks another cup of tea, then he writes $\text{[math]}$ lines and so on: $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , ...

The expression $\text{[math]}$ is regarded as the integral part from dividing number a by number b.

The moment the current value $\text{[math]}$ 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.

Input:

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.

Output:

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

Sample Input:

7 2

Sample Output:

Sample Input:

59 9

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF165B