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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'prime'

class Array
  def make_power
    (0..self[1]).map { |x| self[0] ** x }
  end
end

n, m = gets.split.map(&:to_i)
ps = Prime.prime_division(m)
if ps.size == 1
  ds = ps.map(&:make_power)[0].reverse
else
  ds = ps.map(&:make_power).inject(&:product).map(&:flatten).map { |x| x.inject(:*) }.sort.reverse
end
p ds.bsearch { |x| x <= m / n }