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())
# 問題はM//N>xを満たすようなMの約数xの中で最小のものと読み替えられる。
bdr = M//N
ans = 1

for i in range(1,int(M**0.5+1)):
    if M%i==0:
        yakusu = M//i
        if yakusu<=bdr:
            ans = yakusu
            break
        elif i <= bdr:
            ans = i
print(ans)