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: Wrong Answer)

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

# 割り切れる場合は等分したときの値が最大公約数が一番大きくなる
if m % n == 0
  puts m / n
  exit
end

# 最大10^9ループ
(m / n).downto(1) do |i|
  # n-1個はi, 1個はi+rとなるような数列
  r = m - i * n
  if (i+r) % r == 0
    puts r
    exit
  end
end

puts 1