## Setting

You might remember the definition of the Fibonacci numbers (at this point in your study of computer science, you should have already dreamt of these at least once):

$$f_1 := 1$$

$$f_2 := 2$$

$$f_n := f_{n-1} + f_{n-2}$$

Given two numbers $$a$$ and $$b$$, calculate how many Fibonacci numbers there 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, $$a \leq b \leq 10^{100}$$.

## Output

For each test case output on a single line the number of Fibonacci numbers $$f_i$$ with $$a \leq f_i \leq b$$.

## Sample Input

10 100
1234567890 9876543210
0 0


## Sample Output

5
4


This is challenge 10183 of the ACM International Collegiate Programming Contest. Test input is provided by uDebug.

## Statistics

 Difficulty (2 votes) Average test runtime 0.25 Points (changes over time) 10 Tried by 11 users Solved by 10 users

## Global ranking

# Name Runtime Points worth
1 Pascal 0.14 15
2 Mac 0.15 14
3 ,s/java/NaN/gi 0.15 14
4 贝尔恩德 0.20 11
5 Justin 0.20 11
6 Irfan 0.20 11
7 JB 0.26 8
8 Skøgland 0.32 7
9 AlexanderP 0.41 5
10 IeM 0.43 5