Problem:
Score : 300 points

Problem Statement

There is a box containing N balls. The i-th ball has the integer A_i written on it.
Snuke can perform the following operation any number of times:

Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.

Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq K \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.

Sample Input 1

3 7
9 3 4

Sample Output 1

POSSIBLE

First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE.

Sample Input 2

3 5
6 9 3

Sample Output 2

IMPOSSIBLE

No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.

Sample Input 3

4 11
11 3 7 15

Sample Output 3

POSSIBLE

The box already contains 11 before we do anything. The answer is therefore POSSIBLE.

Sample Input 4

5 12
10 2 8 6 4

Sample Output 4

IMPOSSIBLE

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {
        long[] inpt = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
        long num = inpt[1];
        this.Items = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
        string ans = "IMPOSSIBLE";
        if(GetDifff(num)) {
            ans = "POSSIBLE";
        }
        Console.WriteLine(ans);
    }

    private long[] Items;

    private bool GetDifff(long num) {
        Dictionary<long, bool> list = new Dictionary<long, bool>();
        List<long> addList = this.Items.ToList();
        addList.ForEach(a=>list.Add(a, true));
        while(addList.Count > 0) {
            Dictionary<long, bool> nextList = new Dictionary<long, bool>();
            foreach(long num1 in addList) {
                foreach(long num2 in list.Keys) {
                    long tmp = Math.Abs(num1 - num2);
                    if(num1 == tmp) {
                        return true;
                    }
                    if(tmp == num) {
                        return true;
                    }
                    if(tmp == 1) {
                        return true;
                    }
                    if(!list.ContainsKey(tmp)) {
                        nextList[tmp] = true;
                    }
                }
            }
			addList = nextList.Keys.ToList();
            addList.ForEach(a=>list.Add(a, true));
        }
        return false;
    }


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"



3 5
6 9 3


";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}