Description

Starting from a positive integer $N$, find the smallest positive integer that is not divisible by $N$. If we repeat this process using the obtained positive integer, we will eventually get $2$.

Define $\operatorname{strength}(N)$ as the length of the resulting sequence. For example, for $N = 6$, we can obtain the sequence $6,4,3,2$, which consists of $4$ numbers, so $\operatorname{strength}(6) = 4$.

Given two positive integers $A, B$, compute:

Input Format

The input consists of one line containing two integers $A, B$ separated by a space.

Output Format

Output one integer on a single line, representing the result.

3 6

11

100 200

262

Hint

Constraints

For $100\%$ of the testdata, it is guaranteed that $3 \le A < B \le 10^{17}$.

Notes

The scoring for this problem follows the original COCI settings, with a full score of $140$.

Translated from COCI2012-2013 CONTEST #1 T5 SNAGA.

Translated by ChatGPT 5