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)

N, M = map(int, input().split())
ans = 1

S = M / N
S = int(S)
#print(S)
import math
if N == 1:
    ans = M
else:
    not_sosu = -1
    for i in range(2, int(math.sqrt(M)) + 1):
        if M % i == 0:
            not_sosu = 1
            if M / i >= N and M % i == 0:
                ans = max(ans, i)
            j = M // i
            if M / j >= N and M % j == 0:
                ans = max(ans, j)
            #print(i)
    if not_sosu == -1:
        ans = 1