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 Python (3.4.3) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
"""
D - Partition
https://atcoder.jp/contests/abc112/tasks/abc112_d

"""
import sys


from bisect import bisect_right

def solve(N, M):
    def divisor(N):
        divisors = set()
        for i in range(1, int(N**0.5)+1):
            if N % i == 0:
                divisors.add(i)
                divisors.add(N // i)
        return divisors

    div_M = sorted(list(divisor(M)))
    i = bisect_right(div_M, M/N)
    if i:
        return div_M[i-1]
    else:
        return 1



def main(args):
    N, M = map(int, input().split())
    ans = solve(N, M)
    print(ans)


if __name__ == '__main__':
    main(sys.argv[1:])