How many Fibs?

Time Limit: 1000 ms

Memory Limit: 65535 ms

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<=10^100. 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

10 100
1234567890 9876543210
0 0

Sample Output

5
4

Hint

Source

Ulm Local

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