\(7^{th}\) round, March \(7^{th}\) 2015
Young Bojan, today a successful student of electrical engineering, loved coloring ever since he was a
little boy. Remembering careless days from his childhood, he decided to buy a coloring book and \(K\)
colors and get to work. It’s interesting that Bojan doesn’t like colorful pictures, so he decided to color
each picture using at most three different colors. Additionally, Bojan will never color two adjacent
areas using the same color because, as he puts it, "what’s the use of this line in between then?" Two
areas are considered adjacent if their edges have at least one joint point. For example, areas denoted
with 4 and 3 (see image below) are adjacent, whereas areas 1 and 2 aren’t. Additionally, coloring of
the image below is in accordance with all of Bojan’s demands.
Before he begins coloring a picture, Bojan asks himself in how many ways he can color that picture
so he meets with all his conditions. Given the fact that Bojan is studying electrical engineering, it is
understandable that combinatorics isn’t his strong point, so he asked you for help.

The first and only line of input contains two integers \(N\) (1 ⩽\(N\) ⩽8) and \(K\) (1 ⩽\(K\) ⩽1 000) which
denote the ordinal number of the picture from the coloring book and the number of different colors
Bojan can use, respectively.
You can find the coloring book with the numbered pictures on the next page.

The first and only line of output must contain the number of ways Bojan can color the \(N\)^{th} picture
from the coloring book if he has \(K\) different colors at his disposal. Two colorings are different if they
differ in color in at least one area.

생성자가 기록되지 않았습니다.

출처 COCI 2014/2015 Contest 7