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How many Fibs?

University of Ulm local Contest DE Germany

Timelimit: 3

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].


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.


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

Sample Input Sample Output

10 100
1234567890 9876543210
0 0