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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.stream.Stream;

public class Main {
    private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static PrintWriter pw = new PrintWriter(System.out);
    public static void main(String[] args) throws IOException {
        func();
        pw.flush();
        return;
    }

    static void func() throws IOException {
        int[] input = arrayOfInt();
        int n = input[0];
        int m = input[1];

        int MAX = (int)Math.floor(m/n);
        long ans = 1;
        for(int i = 2;i * i <= m && i <= MAX;i++){
            if (m%i != 0) continue;
            ans = Math.max(ans,i);
            if(m/i <= MAX) ans = Math.max(ans,m/i);
        }
        println(ans);
    }
    // 入力受け取り
    static String next() throws IOException {return br.readLine();}
    static int nextInt() throws IOException{return getInt(br.readLine());}
    static long nextLong() throws IOException{return getLong(br.readLine());}
    static String[] arrayOfString() throws IOException{return br.readLine().split(" ");}
    static int[] arrayOfInt() throws IOException{return toIntArray(arrayOfString());}
    // 変換
    static long getLong(String val) {return Long.parseLong(val);}
    static int getInt(String val) {return Integer.parseInt(val);}
    static int[] toIntArray(String[] array) {return Stream.of(array.clone()).mapToInt(Integer::parseInt).toArray();}
    static String joinToString(String[] array) {
        StringBuilder sb = new StringBuilder();
        for(int i = 0;i < array.length;i++) sb.append(array[i]);
        return sb.toString();
    }

    // 出力
    static void println(Object val){pw.println(val);}
}