Counting cool words

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 $v = 3$ :

aabab ababa babaa toiep zeyui

Remember that there are 5 vowels and 21 consonants.

Input

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

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 $10^{18}$ .

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T11:33:52.892Z