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)

N, M = map(int, input().split())
candidates = []
for p in range(1, max(int(M ** 0.5) + 1, N + 1)):
    if M % p == 0:
        if M // p >= N:
            # p * (M // p = a1+a2+.. >= N) = M
            candidates.append(p)
        if p >= N:
            # (M // p) * (p = a1+a2+.. >= N) = M
            candidates.append(M // p)
print(max(candidates))