Recall the definition of the Fibonacci numbers:

Given two numbersf_{1}:= 1f_{2}:= 2f_{n}:=f_{n-1}+f_{n-2}(n>=3)

**Input Specification**

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

**Output Specification**

For each test case output on a single line the number of Fibonacci numbers
*f _{i}* with

**Sample Input**

10 100 1234567890 9876543210 0 0

**Sample Output**

5 4