Problem:
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.

Sample Input 1

3 14

Sample Output 1

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.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

main=print.solve.map read.words=<<getLine
solve[n,m]
  |v<n=1
  |otherwise=head$[i|i<-reverse[1..m`div`n],m`mod`i==0]
  where v=f 2 m
f i k
  |i*i>k=k
  |r==0=q
  |otherwise=f(i+1)k
  where(q,r)=k`divMod`i