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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
class Main{
 public static void main(String args[]){
Scanner sc=new Scanner(System.in);
int N= sc.nextInt();
int M= sc.nextInt();
int gcd=1;
for(int n=1;n<=M/N;n++) {
   if(N==1) {
	   gcd=M;
	   System.out.println("break");
   break;
   }
   else if(M%n==0) {
	if(n*N<=M) {
	gcd=n;
	 }
    }	
 }
System.out.println(gcd);
 }
  }