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)

from fractions import gcd
N, M = map(int, input().split())
if M%N==0:
  print(M//N)
else:
  c = M%N
  b = M//N
  ls = []
  ans = 0
  x = M
  for i in range(1,(b+1)//2+1):
    x -= N
    if gcd(i,x)>ans:
      ans = gcd(i,x)
  print(ans)