Difference

A *smallest different sequence* (SDS) is a sequence
of positive integers created as follows: $A_1=r \geq 1$. 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, \ldots $ 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 consists of a single line containing two positive integers $A_1$ $m$ ($1 \leq r \leq 100, 1 \leq m \leq 200\, 000\, 000$).

Display the smallest value $n$ such that the sequence $A_1, \ldots , A_ n$ either contains $m$ as a value in the sequence or as a difference between two values in the sequence. All answers will be $\leq 10\, 000$.

Sample Input 1 | Sample Output 1 |
---|---|

1 5 |
4 |

Sample Input 2 | Sample Output 2 |
---|---|

1 12 |
4 |

Sample Input 3 | Sample Output 3 |
---|---|

5 1 |
2 |