Problem:
Score : 200 points

Problem Statement

There are N balls placed in a row.
AtCoDeer the deer is painting each of these in one of the K colors of his paint cans.
For aesthetic reasons, any two adjacent balls must be painted in different colors.

Find the number of the possible ways to paint the balls.

Constraints

1≦N≦1000

2≦K≦1000

The correct answer is at most 2^{31}-1.

Input

The input is given from Standard Input in the following format:

N K

Output

Print the number of the possible ways to paint the balls.

Sample Input 1

2 2

Sample Output 1

2

We will denote the colors by 0 and 1. There are two possible ways: we can either paint the left ball in color 0 and the right ball in color 1, or paint the left in color 1 and the right in color 0.

Sample Input 2

1 10

Sample Output 2

10

Since there is only one ball, we can use any of the ten colors to paint it. Thus, the answer is ten.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

def kkk(v,nest)
  r = 0
  if v!=nil then
    s = sprintf("%d,%d", v,nest)
  end
  return 1 if nest==N
  return $memo[s] if $memo.has_key?(s)
  K.times do |i|
    if v!=nil then
      next if i==v
    end
    r += kkk(i,nest+1)
  end
  $memo[s] = r
  return r
end

N,K = gets.split(/\s/).map {|s|s.to_i}
$memo = Hash.new

puts kkk(nil, 0)