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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
from itertools import combinations as combi
input = sys.stdin.readline
N, M = map(int, input().split())
i = 2
res = 1
while i * i <= M:
  t = 1
  if M % i == 0 and (M // i >= N):
    res = max(res, i)
    t = M // i
  if M % t == 0 and (M // t >= N):
    res = max(res, t)
  i += 1
print(res)