In a sumac sequence, t₁, t₂, .., t_m, each term is an integer greater than or equal 0. Also, each term, starting with the third, is the difference of the preceding two terms (that is, t_n+2 = t_n − t_n+1 for n ≥ 1). The sequence terminates at t_m if t_m−1 < t_m.</p>

For example, if we have 120 and 71, then the sumac sequence generated is as follows:

120, 71, 49, 22, 27.

This is a sumac sequence of length 5.

입력 형식

The input will be two positive numbers t₁ and t₂, with 0 < t₂ < t₁ < 10000.

출력 형식

The output will be the length of the sumac sequence given by the starting numbers t₁ and t₂.

예제 입력

120
71

예제 출력

5