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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import math
import sys

def solve(x):
    return M % x == 0

# The method to fix border
def fixBorder(m):
    if not solve(m) and solve(m+1):
        return m+1
    elif not solve(m) and solve(m-1):
        return m-1
    else:
        return m

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

if M % N == 0:
    print(M//N)
    sys.exit()

l = 1
r = 10**10
m = math.ceil((l+r)/2)

while l <= r:
    m = math.ceil((l+r)/2)
    # print(l, r, m)

    if solve(m):
        # print('too small!')
        l = m+1
    else:
        # print('too big!')
        r = m-1

# print(m)
print(fixBorder(m))