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)

# coding: utf-8
import math

N, M = [int(s) for s in input().strip().split()]

if N == 1:
    print(M)
    exit()

ROOT_M = int(math.sqrt(M))
divisors = []
for d in range(1, ROOT_M+1):
    if M % d == 0:
        divisors.append(d)
        divisors.append(M//d)

max_gcd = max([d for d in divisors if d > M/N])
print(max_gcd)