Write a program that prints the number of sequences
made up of exactly *z* zeros and *u* ones
that do not contain two consecutive zeros nor three consecutive ones.

For instance, there are 8 sequences for *z* = 3 and *u* = 4:

0101011 0101101 0110101 0110110 1010101 1010110 1011010 1101010 |

**Input**

Input consists of several pairs of natural numbers *z* and *u*,
each between 0 and 90.

**Output**

For every pair of *z* and *u*, print the required number.

Public test cases

**Input**

0 0 1 1 3 4 65 90

**Output**

1 2 8 2529372610666365912

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++