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'

n, m = gets.chomp.split(' ').map(&:to_i)

factors = Prime.prime_division(m)
i_counts = '1' * factors.map { |a, b| b }.inject(:+)
counts = i_counts.to_i(2)
length = i_counts.size
nums = factors.reverse.map do |a, b|
  Array.new(b) { a }
end.flatten

result = 1
counts.downto(1).each do |i|
  flags = i.to_s(2).rjust(length, '0').chars.map(&:to_i)
  factor = nums.select.with_index(0) { |_, idx| flags[idx] == 1 }.inject(:*)
  rest = nums.select.with_index(0) { |_, idx| flags[idx] == 0 }.inject(:*) || 1

  if rest >= n && factor >= result
    result = factor
  end
end
puts result