Some sequences of bits (2) P34343

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:

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.