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: Accepted)

def main
  n, m = gets.split.map(&:to_i)
  # 割り切れるなら➾即決
  if m % n == 0
    puts m / n
    return
  end

  (m/n).downto(2) do |d|
    next if m % d != 0

    # 割り切れるのでチャンスはあるが、
    # 個数の問題をクリアできるか？
    num = m / d
    if n <= num
      puts d
      return
    end
  end
  puts 1
end

if __FILE__ == $0
  main
end