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: Wrong Answer)


import math


def divisor(x):
    d = [1]
    for i in range(2, math.ceil(math.sqrt(x)) + 1):
        if x % i == 0:
            d.append(i)
    if d[-1] != x:
        d.append(x)
    return d
    


def submit():
    n, m = map(int, input().split())

    # Mの約数を求める
    d = divisor(m)
    nd = len(d)

    # 二分探索で条件を満たすdを求める
    l = 0
    r = nd - 1
    while l <= r:
        mid = (l + r) // 2
        if n * d[mid] <= m:
            l = mid + 1
        else:
            r = mid - 1
    print(d[l - 1])


submit()