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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractMap;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.NoSuchElementException;


public class Main {
	public static void main(String[] args) {
		
		for(int i=0;i<1;i++) {
			
			slover();
			out.flush();
		}
	}
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	

		



		@SuppressWarnings("unused")
		private static class D{

			D(ArrayList<Integer> X,ArrayList<Integer> Y,int t,int index){

			}

		}



	//Set<Long> a=new HashSet<Long>();
	
	
	
	//Integer.toBinaryString(i);
	//Integer.toString(i, 2);
//	//Integer.parseInt(bin, 2);
	//bitset
		//StringBuffer S = new StringBuffer(sc.next());
				//String hoge2 = str.reverse().toString();
				//map.containsKey(A)
				//Map<Integer, Integer> map = new HashMap<Integer, Integer>(N);
				/*for ( キーのデータ型 key : マップの名前.keySet() ) {
					データのデータ型 data = マップの名前.get( key );

					// keyやdataを使った処理;
				}*/
				//int i = Integer.parseInt(s);
				//Queue<String> qq=new ArrayDeque<>(); //add,poll,peek BFSは前から実行される
				//Deque<String> dd=new ArrayDeque<>();//push後ろに入れる,poll(pop)後ろからとる,peek addは先頭に入るからバグ注意
				//stackdfsは後ろから実行される
				//ArrayList<Integer> cc = new ArrayList<>(N);
				//cc.contains(tmp)
				//Arrays.asList(c).contains("a")
				//list.set(1,"walk");//1 1 2 3 5
				//PriorityQueue<Integer> r=new PriorityQueue<Integer>();//add poll
		
		public static class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> implements Comparable<Pair<K, V>> {
			/** serialVersionUID. */
		    private static final long serialVersionUID = 6411527075103472113L;
	 
		    public Pair(final K key, final V value) {
		        super(key, value);
		    }
	 
			@Override
			public int compareTo(Pair<K, V> o) {
	 
				Comparable key = (Comparable)this.getKey();
				Comparable key2 = (Comparable)o.getKey();
	 
				return key.compareTo(key2);
			}
	 
		}
	 
		// 文字列として入力を取得
		
		
		
		
	private static long mod=1000000007;
	private static int INF =999999999;
	@SuppressWarnings("unused")
	private static long LINF=4000000000000000000L;
	
	@SuppressWarnings("unused")
	private static long ncr(long n,long r) {
		long res=1;
		
		for(int i=0;i<r;i++) {
			res*=n-i;
			res/=i+1;
		}
		return res;
	}
	@SuppressWarnings("unused")
	private static int StringCount(String T,String v) {
		int res=0;
		int t=0;
		while(T.indexOf(v,t)>=0) {
			//p(t);
			res++;
			t=T.indexOf(v,t)+1;
		}
		return res;
	}
	
	private static int slover()   {
		
		int N=sc.nextInt(),K=sc.nextInt();
		int A[]=sc.nextIntArray(N, false);
		int t=A[0];
		int max=0;
	
		for(int i=0;i<N;i++) {
			t=(int) gcd(A[i],t);
			max=Math.max(max, A[i]);
		}
		p(K%t==0&&K<=max ? "POSSIBLE":"IMPOSSIBLE");
		
		
		return 0;
	}
	@SuppressWarnings("unused")
	private static void shape(int Q[]) {
		for(int i=0;i<Q.length;i++) {
			find2(Q,i);
		}
	}
	private static int find2(int Q[],int a) {
		//aの根をbの根にする。
		if(Q[a]==a) {
			return Q[a];
		}else {
			return Q[a]=find2(Q,Q[a]);
		}
		
	}
	@SuppressWarnings("unused")
	private static void union2(int Q[],int a,int b) {
		
		int root1=find2(Q,a);
		int root2=find2(Q,b);
		Q[root1]=Q[root2];
	}
	
	
	@SuppressWarnings("unused")
	private static void set_add(int Q[],int index,int value) {
		if(Q[index]==value) {
			
		}
		else if(Q[index]==INF) {
			Q[index]=value;
			
		}else if(value<Q[index]) {
			set_add(Q,index*2+1,value);
		}else {
			set_add(Q,index*2+2,value);
		}
	}
	
	@SuppressWarnings("unused")
	private static void priority_queue_add(int Queue[],int index,int value) {
		Queue[index]=value;
		
		if(index!=0) {
			if((index-1)/2>=0&&Queue[(index-1)/2]>value) {
				Queue[index]=Queue[(index-1)/2];
				priority_queue_add(Queue,(index-1)/2,value);
				
			}
			if((index-2)/2>=0&&Queue[(index-2)/2]>value) {
				Queue[index]=Queue[(index-2)/2];
				priority_queue_add(Queue,(index-2)/2,value);
				
			}
		}
		
		
	}
@SuppressWarnings("unused")
private static int priority_queue_getFirst(int[] Queue) {
		int res=Queue[0];
		Queue[0]=Queue[Queue.length-1];
		Queue[Queue.length-1]=INF;
		//System.out.println(Arrays.toString(Queue));
		//大きさのチェック
		Q_shape(Queue,0);
		
		return res;
	}
	private static void Q_shape(int[] Queue,int index) {
			
			
		
			if(index*2+1<Queue.length&&Queue[index*2+1]<Queue[index]) {
				int v=Queue[index];
				Queue[index]=Queue[index*2+1];
				Queue[index*2+1]=v;
				Q_shape(Queue,index*2+1);
				
			}
			if(index*2+2<Queue.length&&Queue[index*2+2]<Queue[index]) {
				int v=Queue[index];
				Queue[index]=Queue[index*2+2];
				Queue[index*2+2]=v;
				Q_shape(Queue,index*2+2);
				
			}
		
		
		
	}
	private static int union_MaxSize(int[] tree) {
		
		union_shape(tree);
		
		int V[]=new int[tree.length+1];
		
		for(int i=0;i<tree.length;i++) {
			V[tree[i]]++;
		}
		int max=0;
		for(int i=0;i<=tree.length;i++) {
			max=Math.max(max, V[i]);
		}
		return max;
	}
	
	public static int find(int[] tree,int idx) {
        if(tree[idx]==idx) return idx;
        else {
        	
        	return tree[idx] = find(tree,tree[idx]);
        }
    }
	public static void union_shape(int[] tree) {
		for(int i=0;i<tree.length;i++) {
			find(tree,i);
		}
	}

    //union idx2 tree to idx1 tree O(a(N))
    public static int[] union(int tree[],int idx1,int idx2) {
        int root1 = find(tree,idx1);
        int root2 = find(tree,idx2);
        tree[root2] = root1;
        return tree;
    }
	private static boolean heihou(long T) {
		if(Math.pow((int)Math.sqrt(T), 2)==T)return true;
		return false;
	}
	private static String zeroume(String S) {
		while(S.length()<6)S='0'+S;
		return S;
	}
	
	//速度が足りないときは、前計算を1回だけにしたり、longをintに変えたりするといい
	private static long modNcR2(int n,int r) {
		long x_b=1;
		
		for(int i=0;i<r;i++) {
			x_b*=(n-i);
			x_b%=mod;
		}
		
		long y=1;
		for(int i=1;i<=r;i++) {
			y*=i;
			y%=mod;
			//nPrにr!%modの逆元を掛ける
		}
		return  (x_b*modPow((int) y,mod-2,mod)%mod);
		
	}
	
	

	
	
	
	private static long modPow(int i,long t,long mod) {
		//iのt乗をO(log t)で返す
		i%=mod;
		t%=mod;
		long a=i;
		long res=1;
		//for(int i=0;i<S.length();i++) {if(S.charAt(N-i)=='1') {res=res*a%mod;}
		//tをStringで受け取りたい時用
		while(t!=0) {
			if((1&t)==1) {
				res=res*a%mod;
			}
			a=a*a%mod;
			t=t>>1;
		}
		return res;
	}
	
	public static long gcd(long num1,long num2) {
        if(num2==0) return num1;
        else return gcd(num2,num1%num2);
    }
	public static long lcm(long num1,long num2) {
		return num1*num2/gcd(num1,num2);
	}
	//O(N^0.5)
	private static boolean isPrime(long t) {
		if(t<2)return false;
		for(int i=2;i*i<=t;i++) {
			if(t%i==0)return false;
		}
		return true;
	}
	private static ArrayList<Long> Divisors(long t) {
		ArrayList<Long> c=new ArrayList<Long>();
		
		for(long i=1;i*i<=t;i++) {
			if(t%i==0) {
				
				if(i*i!=t) {
					c.add(t/i);
				}
				c.add((long)i);
			}
		}
		return c;
	}
	private static ArrayList<Long> Sorted_Divisors(long t) {
		ArrayList<Long> c=new ArrayList<Long>();
		for(long i=2;i*i<=t;i++) {
			
			
			if(t%i==0) {
				p(t+" "+i);
				c.add((long)i);
				t/=i;
				i--;
			}
		}
		if(t!=1)c.add(t);
		Collections.sort(c);
		
		return c;
	}
	private static void bubunwa() {
		int N=sc.nextInt();
		int K=sc.nextInt();
		int a[]=sc.nextIntArray(N, false);

		boolean dp[] =new boolean[K+1];

		Arrays.fill(dp, false);
		dp[0]=true;
		for(int i=0;i<N;i++) {
			for(int x=K-a[i];x>=0;x--) {
				if(dp[x])dp[x+a[i]]=true;
			}
		}

		p(dp[K] ? "Yes":"No");
	}
	
	private static String bitToString(int i) {
		return Integer.toBinaryString(i);
	}
/*********************************************************************/
	//target以下までの値のindexを返す
	//target以上が欲しいときは返り値+1すればいい
	//0-indexで個数を求めるときはさらにindex+1する必要あり
	private static int lower_bound(long a[],long target) {
	//p(target+ " "+Arrays.toString(a));
	if(a[0]>target)return -1;
	//最後の値がtarget以下であるときは最後のindexを返す。
	//target以上が欲しいときは注意する必要あり
	if(a[a.length-1]<=target) return a.length-1;

	int S=-1;
	int E=a.length;

	while(S<E) {

		int G=(S+E)/2;
		if(G+1==a.length) {
			G--;
		}
		//未満にしたいときは=の場所を変える
		if(a[G]<=target&&a[G+1]>target) {
			return G;

		}else if(a[G]<=target){
			S=G;
		}else if(a[G]>target) {
			E=G;
		}

	}


	return -1;
	}
	static String nextPermutation(String s) {
		ArrayList<Character> list=new ArrayList<Character>();
		for(int i=0;i<s.length();i++) {
			list.add(s.charAt(i));
		}
		int pivotPos=-1;
		char pivot=0;
		for(int i=list.size()-2;i>=0;i--) {
			if(list.get(i)<list.get(i+1)) {
				pivotPos=i;
				pivot=list.get(i);
				break;
			}
		}
		if(pivotPos==-1&&pivot==0) {
			return "Final";
		}
		int L=pivotPos+1,R=list.size()-1;



		int minPos=-1;
		char min =Character.MAX_VALUE;

		for(int i=R;i>=L;i--) {
			if(pivot<list.get(i)) {
				if(list.get(i)<min) {
					min=list.get(i);
					minPos=i;
				}
			}
		}

		Collections.swap(list, pivotPos, minPos);
		Collections.sort(list.subList(L, R+1));


		StringBuilder sb=new StringBuilder();
		for(int i=0;i<list.size();i++) {
			sb.append(list.get(i));
		}
		return sb.toString();
	}
private static long[][] com;
private static void nCr() {
	int MAX = 3001;
	com= new long[MAX][MAX];
	for(int i = 0; i < MAX; i++)
	    com[i][0] = 1;
	for(int i = 1; i < MAX; i++) {
	    for(int j = 1; j <= i; j++) {
	        com[i][j] = com[i-1][j-1] + com[i-1][j];
	        com[i][j] %= mod;
	    }
	}
}


	static void p(String ans) {out.println(ans);}
	static void p(int ans) {out.println(ans);}
	static void p() {out.println();}
	static void p(long ans) {out.println(ans);}
	static void p(double ans) {out.println(ans);}
	static void p(boolean ans) {out.println(ans);}
	
	
	static void pn(String ans) {out.print(ans);};
	static void pn(int ans) {out.print(ans);};
	static void pn() {out.print("");};
	static void pn(long ans) {out.print(ans);};
	static void pn(double ans) {out.print(ans);};

	static class FastScanner {
	    private final InputStream in = System.in;
	    private final byte[] buffer = new byte[1024];
	    private int ptr = 0;
	    private int buflen = 0;

	    private boolean hasNextByte() {
	      if (ptr < buflen) {
	        return true;
	      } else {
	        ptr = 0;
	        try {
	          buflen = in.read(buffer);
	        } catch (IOException e) {
	          e.printStackTrace();
	        }
	        if (buflen <= 0) {
	          return false;
	        }
	      }
	      return true;
	    }

	    private int readByte() {
	      if (hasNextByte()) return buffer[ptr++];
	      else return -1;
	    }

	    private static boolean isPrintableChar(int c) {
	      return 33 <= c && c <= 126;
	    }

	    private void skipUnprintable() {
	      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
	    }

	    public boolean hasNext() {
	      skipUnprintable();
	      return hasNextByte();
	    }

	    public String next() {
	      if (!hasNext()) throw new NoSuchElementException();
	      StringBuilder sb = new StringBuilder();
	      int b = readByte();
	      while (isPrintableChar(b)) {
	        sb.appendCodePoint(b);
	        b = readByte();
	      }
	      return sb.toString();
	    }

	    public long nextLong() {
	      if (!hasNext()) throw new NoSuchElementException();
	      long n = 0;
	      boolean minus = false;
	      int b = readByte();
	      if (b == '-') {
	        minus = true;
	        b = readByte();
	      }
	      if (b < '0' || '9' < b) {
	        throw new NumberFormatException();
	      }
	      while (true) {
	        if ('0' <= b && b <= '9') {
	          n *= 10;
	          n += b - '0';
	        } else if (b == -1 || !isPrintableChar(b)) {
	          return minus ? -n : n;
	        } else {
	          throw new NumberFormatException();
	        }
	        b = readByte();
	      }
	    }

	    public int nextInt() {
	      return (int) nextLong();
	    }

	    public double nextDouble(){
	    	return Double.parseDouble(next());
	    }

	    public int[] nextIntArray(int N, boolean oneBased) {
	      if (oneBased) {
	        int[] array = new int[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      } else {
	        int[] array = new int[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      }
	    }

	    public long[] nextLongArray(int N, boolean oneBased) {
	      if (oneBased) {
	        long[] array = new long[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      } else {
	        long[] array = new long[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      }
	    }
	  }
}