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.

Example

Input:

10 100
1234567890 9876543210
0 0

Output:

5
4

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