bee 1722 - How many Fibs?

Recall the definition of the Fibonacci numbers:

f₁ = 1

f₂ = 2

f_n = f_n-1 + f_n-2 (n ≥ 3)

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a,b].

Input

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a = b = 0.Otherwise, a ≤ b ≤10¹⁰⁰. The numbers a and b are given with no superfluous leading zeros.

Output

For each test case output on a single line the number of Fibonacci numbers fi with a ≤ fi ≤ b.

Sample Input	Sample Output
10 100 1234567890 9876543210 0 0	5 4