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)

N, M = map(int, input().split())

def primefactorize(n):
    fct = []  # return [[p1, power1], [p2, power2], ...]
    p, power = 2, 0
    while p * p <= n:
        while n % p == 0:
            n = n // p
            power += 1
        if power > 0:
            fct.append([p, power])
        if p == 2:
            p += 1
        else:
            p += 2
        power = 0
    if n > 1:
        fct.append([n, 1])
    return fct

def divisorize(fct):
    b, e = fct.pop()  # base, exponent
    pre_div = divisorize(fct) if fct else [[]]
    suf_div = [[(b, k)] for k in range(e + 1)]
    return [pre + suf for pre in pre_div for suf in suf_div]

def num(fct):
    a = 1
    for base, exponent in fct:
        a = a * base**exponent
    return a

fct = primefactorize(M)
factors = []
for div in divisorize(fct):
    factors.append(num(div))

factors.sort()
cd = 0
k = M/N
for x in factors:
    if x <= k:
        cd = max(cd, x)
print(cd)