National Olympiad in Informatics, China, 1999

July 17^th is Mr. W's Birthday, and ACM-THU would like to create for him a birthday cake with volume $N\pi$, comprised of $M$ cylindrical layers.

Counting upwards from the bottom layer, the $i$-th $(1\le i\le M)$ layer of cake is a cylinder with a radius of $R_i$ and a height of $H_i$. When $i<M$, we require for $R_i>R_{i+1}$ and $H_i>H_{i+1}$.

To reduce the money spent on icing the cake, we would like to minimize $Q$, the outer surface area of the cake (not including the bottom surface of the bottommost layer).

Let $Q=S\pi$. Please write a program that, given $N$ and $M$, finds a strategy to construct the cake (with appropriate $R_i$ and $H_i$ values) that minimizes the value of $S$.

Other than $Q$, all values described above will be positive integers.

Input Specification

The input will consist of two lines. The first line is the integer $N$ $(N\le 10000)$, indicating that the volume of the cake is $N\pi$. The second line of input is the integer $M$ $(M\le 20)$, representing the number of levels in the cake.

Output Specification

The output should consist of one line - a positive integer $S$ (if no answer, $S=0$).

Sample Input

100
2

Sample Output

68

Formulas for cylinders:

Volume: $V=\pi R^{2}H$
Side surface area: $A^{\prime }=2\pi RH$
Bottom surface area: $A=\pi R^2$

Problem translated to English by Alex.