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 (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor :a, :b, :n, :m, :h, :w, :ans
  def initialize
    @n, @m = gets.to_s.split.map{ |v| v.to_i }
    @ans = 0
  end

  def solve
    calc
    puts ans
  end

  def top
    @top ||= Math.sqrt(m).to_i
  end

  def chmax(v)
    @ans = v if @ans < v
  end

  def calc
    each_div do |i,j|
      chmax(i) if j >= n
      chmax(j) if i >= n
    end
  end

  def each_div
    1.upto(top) do |i|
      next if m % i != 0
      j = m / i
      yield i, j
      yield j, i
    end
  end
end

pb = Problem.new
pb.solve