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)

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

# 最大公約数をmax_mとすると a_1, a_2, ..., a_n はすべてmax_mで割り切れるので
# m = a_1 + a_2 + ... + a_n もmax_mで割り切れる

# 最大10^9ループ
(m / n).downto(1) do |i|
  if m % i == 0
    puts i
    exit
  end
end