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)

#!/usr/bin/env python3
import sys
import bisect
from math import *
from itertools import *
from collections import *
from functools import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, M: int):
    ds = []
    for i in range(1, int(ceil(sqrt(M))) + 1):
        if M % i == 0:
            ds.append(i)
            ds.append(M // i)
    ds.sort()
  
    th = M // N
    return ds[bisect.bisect(ds, th)-1]


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    result = solve(N, M)
    print(result)

if __name__ == '__main__':
    main()