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++ Python