SPOJ Problem Set (practice) 536. How many Fibs Problem code: TFIB

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 f_i with a<=f_i<=b.

Example

Input:

10 100
1234567890 9876543210
0 0

Output:

5
4

---

Added by:	Adrian Kuegel
Date:	2005-07-05
Time limit:	10s
Source limit:	50000B
Languages:	All except: C++ 4.3.2 CLOJ ERL F# GO JS PERL 6 PYTH 3.1.2 SCALA TCL TECS
Resource:	University of Ulm Local Contest 2000