Some sequences of bits (2)

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 $u = 4$ : $0101011 \quad 0101101 \quad 0110101 \quad 0110110 \quad 1010101 \quad 1010110 \quad 1011010 \quad 1101010$

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:21:21.386Z