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