Asmallest 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
Input consists of a single line containing two positive integers$A_1$$m$ ($1 \leq r \leq 100, 1 \leq m \leq 200\, 000\, 000$).
Output
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 |
