In a sumac sequence, t$_1$,t$_2$,…,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$_m$ .

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.

Input Specification

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

Output Specification

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

Sample Input

120
71

Output for Sample Input

5