Counting cool words P67933

In this problems, we say that a word is cool if it does not have two consecutive consonants. Write a program to compute how many words with n lowercase letters, v of which are vowels, are cool.

For instance, these are some of the many cool words for n = 5 and v = 3:

Remember that there are 5 vowels and 21 consonants.

Input

Input consists of several cases, each with two natural numbers 1 ≤ n ≤ 15 and 0 ≤ v ≤ n.

Output

For every case, print the number of cool words with n lowercase letters, v of which are vowels. This number is always smaller than 10¹⁸.