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 ≤ 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 10^{18}.

Public test cases

**Input**

1 0 1 1 2 0 2 1 2 2 3 0 3 1 3 2 3 3 5 3 15 9 15 6 15 15

**Output**

21 5 0 210 25 0 2205 1575 125 330750 35177510566406250 0 30517578125

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++