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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public final class Main {

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int m = fs.nextInt();
        int res = 0;
        for (int p = 1; p * p <= m; p++) {
            if(m % p == 0) {
                if(p <= n) {
                    res = Math.max(res, p);
                }
                if(m/p <= n) {
                    res = Math.max(res, m / p);
                }
            }
        }
        System.out.println(res);
    }

    static final class Utils {
        public static void shuffleSort(int[] arr) {
            shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffleSort(long[] arr) {
            shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffle(int[] arr) {
            final Random r = new Random();

            for (int i = 0; i <= arr.length - 2; i++) {
                final int j = i + r.nextInt(arr.length - i);
                swap(arr, i, j);
            }
        }

        public static void shuffle(long[] arr) {
            final Random r = new Random();

            for (int i = 0; i <= arr.length - 2; i++) {
                final int j = i + r.nextInt(arr.length - i);
                swap(arr, i, j);
            }
        }

        public static void swap(int[] arr, int i, int j) {
            final int t = arr[i];
            arr[i] = arr[j];
            arr[j] = t;
        }

        public static void swap(long[] arr, int i, int j) {
            final long t = arr[i];
            arr[i] = arr[j];
            arr[j] = t;
        }

        private Utils() {}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int[] nextIntArray(int n) {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++) { a[i] = nextInt(); }
            return a;
        }

        long[] nextLongArray(int n) {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++) { a[i] = nextLong(); }
            return a;
        }
    }
}