Problem A
Difference

A smallest different sequence (SDS) is a sequence of positive integers created as follows: $A_1=r\ge 1$. For $n>1$, $A_n=A_{n-1}+d$, where $d$ is the smallest positive integer not yet appearing as a value in the sequence or as a difference between two values already in the sequence. For example, if $A_1=1$, then since $2$ is the smallest number not in our sequence so far, $A_2=A_1+2=3$. Likewise $A_3=7$, since $1,2$ and $3$ are already accounted for, either as values in the sequence, or as a difference between two values. Continuing, we have $1,2,3,4,6$, and $7$ accounted for, leaving $5$ as our next smallest difference; thus $A_4=12$. The next few values in this SDS are $20,30,44,59,75,96,\dots$ For a positive integer $m$, you are to determine where in the SDS $m$ first appears, either as a value in the SDS or as a difference between two values in the SDS. In the above SDS, $12,5,9$ and $11$ first appear in step $4$.

Input

Input consists of a single line containing two positive integers $A_1$ $m$ ($1\le r\le 100,1\le m\le 200000000$).

Output

Display the smallest value $n$ such that the sequence $A_1,\dots ,A_n$ either contains $m$ as a value in the sequence or as a difference between two values in the sequence. All answers will be $\le 10000$.

1 5

4

1 12

4

5 1

2