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)

from math import *

def main():
    N, M = map(int, input().split())
    special_value = M//N
    divisor_set = set(i for i in range(1, (int(sqrt(M)) + 1)) if (M % i == 0))
    divisor_set = divisor_set.union(M//j for j in divisor_set)
    print(int(max(divisor_set, key=lambda x: x if special_value >= x else -1)))

    return

if __name__ == "__main__":
    main()