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# How many Fibs?

**Timelimit: 3**

University of Ulm local Contest Germany

Recall the definition of the Fibonacci numbers:

f_{1} = 1

f_{2} = 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].

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.

For each test case output on a single line the number of Fibonacci numbers **fi** with **a** ≤ **fi** ≤ **b**.

Sample Input | Sample Output |

10 100 |
5 |