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: Runtime Error)

import bisect
n,m=map(int,input().split())
def enum_dif(n):
    ret=[]
    i=1
    while i*i<=n:
        if(n%i==0):
            ret.append(i);
            if(i!=1 and i*i != n):
                ret.append(n//i)
        i+=1
    return ret
enum=enum_dif(m)
enum.sort()
# print(enum)
ind=bisect.bisect_left(enum,m//n)
if(enum[ind]==m//n):
    print(enum[ind])
elif(ind==0):
    print(enum[ind])
else:
    print(enum[ind-1])