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 (7.3.0) (judge verdict: Accepted)

import sys
def factors(n):
  a = []
  x = 1
  while x * x <= n :
    if n % x == 0:          
      a.append(x)
      a.append(n//x)
    x += 1
  return a
n,m=map(int,input().split())
fac=factors(m)
fac.sort()
for i in range(len(fac)-1,-1,-1):
  if n*fac[i]<=m:
    print(fac[i])
    sys.exit()