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: Accepted)

N,M=[int(x) for x in str(input()).split()]
count=0
ans=[]
for i in range(1,int(M**0.5+2)):
  #print(i)
  if M%i==0 and i>=N:
    count=1
    ans.append(M//i)
    break

for i in range(1,int(M**0.5+2)):
  #print(i)
  if M%i==0 and M//i>=N:
    ans.append(i)
print(max(ans))