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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
  
public class Main {
	
    public static void main(String[] args) throws IOException {
        new Main().exec();
    }
    
    public void exec() throws IOException {
    	InputUtil in = new InputUtil();
        PrintWriter out = new PrintWriter(System.out);
    	
        int N = in.nextInt();
    	int K = in.nextInt();
    	int[] A = in.nextInt(new int[N]);
    	
    	int gcd = A[0];
    	int max = A[0];
    	boolean existsK = false;
    	for(int i=1; i<N; i++) {
    		if(A[i] == K){
    			existsK = true;
    			break;
    		}
    		if(gcd>1){
    			gcd = getGcd(gcd,A[i]);
    			if(gcd==1)
    				break;
    		}
    		max = Math.max(max, A[i]);
    	}
        out.println((existsK || (K%gcd==0 && K<max))?"POSSIBLE":"IMPOSSIBLE");
    	out.flush();
    }
    
    public int getGcd(int a, int b) {
    	int tmp;
    	if(a < b) {
    		tmp=a; a=b;b=tmp;
    	}
    	while (a%b != 0){
    		tmp = a%b;
    		if(tmp > b){
        		a = tmp;
    		} else {
    			a = b;
    			b = tmp;
    		}
    	}
    	return b;
    }
}




/**
 * --------------------------------------------------
 * Input Utility
 * --------------------------------------------------
 */
class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 50000;
	
	//Fields
	protected InputStream in;
	private char[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private BufferedReader br = null;
	
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {br = new BufferedReader(new InputStreamReader(this.in = in));}
	protected void initBuf(int bufsiz) {buf = new char[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && br.ready()) {
			max = br.read(buf);
			ptr = 0;
		}
	}

	//Number Input Reader/Parser
	private boolean isNum(char b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(char b) {return b=='-'; }

	private int _nextInt() throws IOException {
		int sign = 1;
		int res = 0;
		char c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public int nextInt() throws IOException {
		readBuf();
		return _nextInt();
	}

	public int[] nextInt(int[] result) throws IOException {
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextInt();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}