Rock-Paper-Scissors

Time limit

Memory limit

128 MB

Problem

Dongju and Hangseung play at most N rounds of rock-paper-scissors. Each player's number of round wins is counted separately, and the first player to win K rounds wins the whole game.

Find the probability that Hangseung wins against Dongju. In every round, both players independently choose rock, paper, or scissors with equal probability.

Input

The first line contains two integers N and K separated by a space. (1 <= K <= N <= 40)

Output

If Hangseung's winning probability is A/B, print A and B separated by a space. A and B must be positive coprime integers.