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: Accepted)

import bisect
import math
import sys
input = sys.stdin.readline

N, M = map(int, input().split())
if M % N == 0:
    print(M//N)
else:
    upper = math.ceil(M/N)
    factor = set()
    for i in range(1, int(M**0.5)+1):
        if M % i == 0:
            factor.add(i)
    
    factor1 = set()
    for i in factor:
        factor1.add(M//i)
    factor |= factor1
    
    factor = sorted(list(factor))
    print(factor[bisect.bisect_right(factor, upper)-1])