D - Partition

Score : $400$ points

Problem Statement

You are given integers $N$ and $M$.

Consider a sequence $a$ of length $N$ consisting of positive integers such that $a_1 + a_2 + ... + a_N$ = $M$. Find the maximum possible value of the greatest common divisor of $a_1, a_2, ..., a_N$.

Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $N \leq M \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the maximum possible value of the greatest common divisor of a sequence $a_1, a_2, ..., a_N$ that satisfies the condition.

3 14

2

Consider the sequence $(a_1, a_2, a_3) = (2, 4, 8)$. Their greatest common divisor is $2$, and this is the maximum value.

10 123

3

100000 1000000000

10000