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: Wrong Answer)

import sys

def main():
  input = sys.stdin.readline
  N, M = map(int, input().split())
  O = [0, 1] + [0 for _ in range(int(M**0.5)+1)]
  H = 1
  for i in range(int(M**0.5)+1, 2, -1):
    while M % i == 0:
      if (M // i) < N:
        break
      else:
        M //= i
        H *= i
  print(H)

if __name__ == '__main__':
  main()