How many Fibs?

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

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].

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 aand 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

10 100
1234567890 9876543210
0 0

Sample Output

5
4

Hint


Source

2000/2001 University of Ulm Local Contest