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: Runtime Error)


def solve(N, M):
    ans = []
    for X in range(2, M):
        S = (N * (N + 1) // 2) * X
        # print(f"X={X}, S={S}, M={M}")
        if (M - S) % X == 0:
            ans.append(X)
            # print(f"ans append : {X}")
        elif S > M:
            # print(f"X={X}, S={S}, M={M}")
            break
    return ans[-1]

if __name__ == "__main__":
    l = input().split(" ")
    N, M = int(l[0]), int(l[1])
    print(solve(N, M))