HDU ACM 1316



Problem Descr iption

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. -Problem Descr iption

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.