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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC112.D();
        }
        class ABC112
        {
            public static void A()
            {
                var N = Read.Int();
                if (N == 1) { Console.WriteLine("Hello World"); return; }
                Console.WriteLine(Read.Int() + Read.Int());
            }
            public static void B()
            {
                var N = Read.Int();
                var T = Read.Int();
                var CT = Read.TupleInt(N);
                var ok = CT.Where(x => x.Item2 <= T).OrderBy(x => x.Item1);
                Console.WriteLine(ok.Count() == 0 ? "TLE" : ok.First().Item1.ToString());
            }
            public static void C()
            {
                var N = Read.Int();
                var XYH = new List<int[]>();
                for(int i = 0; i < N; ++i)
                {
                    XYH.Add(Read.IntN());
                }
                for(int cx = 0; cx <= 100; ++cx)
                {
                    for(int cy = 0; cy <= 100; ++cy)
                    {
                        int h = 0;
                        foreach(var xyh in XYH)
                        {
                            if (xyh[2] > 0)
                            {
                                h = xyh[2] + Math.Abs(xyh[0] - cx) + Math.Abs(xyh[1] - cy);
                                break;
                            }
                        }
                        bool ok = true;
                        foreach(var xyh in XYH)
                        {
                            if(xyh[2] != Math.Max(0,h- Math.Abs(xyh[0] - cx) - Math.Abs(xyh[1] - cy)))
                            {
                                ok = false;
                                break;
                            }
                        }
                        if (ok)
                        {
                            Console.WriteLine("{0} {1} {2}", cx, cy, h); return;
                        }
                    }
                }
            }
            public static void D()
            {
                var N = Read.Int();
                var M = Read.Int();
                var div = Util.Divisor(M);
                var max = div.Where(x => x <= M / N).Max();
                Console.WriteLine(max);
            }
        }


        class Util
        {
            public static HashSet<long> Divisor(long x)
            {
                var div = new HashSet<long>(); for (long p = 1; p * p <= x; ++p) { if (x % p == 0) { div.Add(p); } }
                foreach(var d in div.ToArray())
                {
                    if (!div.Contains(x / d)) { div.Add(x / d); }
                }
                return div;
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
        }
    }
}