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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.SplittableRandom;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * 
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class TaskA
    {
        public void solve(int testNumber, FastReader in, PrintWriter out) 
        {
        	int n=in.nextInt();
        	int k=in.nextInt();
        	int max=0;
        	int gcd=0;
        	for(int i=0;i<n;i++)
        	{
        		int a=in.nextInt();
        		max=Math.max(max,a);
        		gcd=findGcd(gcd,a);
        	}
        	
        	if(k<=max&&k%gcd==0) {
        		out.println("POSSIBLE");
        	}
        	else {
        		out.println("IMPOSSIBLE");
        	}
 
        }
        
        private int findGcd(int a,int b)
        {
        	while(b>0)
        	{
        		int t=a%b;
        		a=b;
        		b=t;
        	}
        	return a;
        }
    }
 
 
 
    static class FastReader
    {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;
 
        public FastReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        private int pread() 
        {
            if (pnumChars == -1)
            {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars)
            {
                curChar = 0;
                try
                {
                    pnumChars = stream.read(buf);
                } catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0)
                {
                    return -1;
                }
            }
            return buf[curChar++];
        }
 
        public int nextInt()
        {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do
            {
                if (c == ',')
                {
                    c = pread();
                }
                if (c < '0' || c > '9')
                {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString()
        {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            StringBuilder res = new StringBuilder();
            do 
	{
                res.appendCodePoint(c);
                c = pread();
                } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public long nextLong()
        {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = pread();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9') 
                {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long[] nextLongArray(int n)
        {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
            {
                array[i] = nextLong();
            }
            return array;
        }
 
        private boolean isSpaceChar(int c)
        {
            if (filter != null)
            {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }
 
        private static boolean isWhitespace(int c) 
        {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
 
        }
 
    }
}