How Many Fibs?

Recall the definition of the Fibonacci numbers:
f1 := 1
f2 := 2
fn := fn-1 + fn-2 (n >= 3)

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

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 <= 10^100. The numbers a and b are given with no superfluous leading zeros.

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

10 100
1234567890 9876543210
0 0

5
4

University of Ulm Local Contest 2000