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: Time Limit Exceeded)

require "prime"

N, M = STDIN.gets.chomp.split(" ").map(&:to_i)

primes = Prime.prime_division(M).select{|prime| prime[0] <= M / N}.map{|prime| Array.new(prime[1], prime[0])}.flatten

divs = [1, M] + (1..primes.size).map{|num| primes.combination(num).map{|prime| prime.inject{|acc, p| acc *= p}}}.flatten

answer = divs.uniq.select{|div| div <= M / N}.max
puts answer