0323. How many Fibs?

Input file name:	fibs.in
Output file name:	fibs.out
Time limit:	2 s
Memory limit:	256 megabytes

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 Specification

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 Specification

For each test case output on a single line the number of Fibonacci numbers f_i with a<=f_i<=b.

Sample Input

10 100
1234567890 9876543210
0 0

Sample Output

5
4

Source: Ulm University Local Contest 2000

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