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.*;
import java.lang.reflect.Array;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class Main {
	private InputStream is;
	private PrintWriter out;
	int time = 0, dp[][], DP[][], dist[], prime[], start[], parent[], end[],
			val[], black[], arr[], arr1[][];
	long MOD = (long) (1e9 + 7);
	ArrayList<Integer>[] amp;
	boolean b[], b1[];
	Pair prr1[];
	char ch[][], c[];
	HashSet<Integer> hs1 = new HashSet<>(), hs2 = new HashSet<>();

	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
			public void run() {
				try {

					// new Main().soln();
				} catch (Exception e) {
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
		new Main().soln();
	}

	int MAX = 1000010, N, K;
	double Q = 1;
	double a = 1, fa = 0;
	long B = 0;
	PriorityQueue<Pair> pq;
	int Dp[][] = new int[1010][1010];
	int MOD1 = 1000000007, MOD2 = 1000000009;

	void solve() {
		int n = ni(), k = ni();
		int arr[] = na(n);
		Arrays.sort(arr);
		if(arr[n-1]<k) {System.out.println("IMPOSSIBLE");return;}
		for(int i = 1; i < n ;i++){
			if((arr[i]!=k) && (arr[i]==(arr[i-1]+arr[0]))) continue;
			else{
				System.out.println("POSSIBLE");
				return;
			}
		}
		if(arr[0]==1 || arr[0]==k) System.out.println("POSSIBLE");
		else System.out.println("IMPOSSIBLE");
	}
	int dfs(int x) {
		b[x] = true;
		int res = 0;
		for (int i : amp[x]) {
			if (!b[i]) {
				res ^= (1 + dfs(i));
			}
		}
		return (res);
	}

	void buildGraph(int n) {
		while (n-- > 0) {
			int x = ni() - 1, y = ni() - 1;
			amp[x].add(y);
			amp[y].add(x);
		}
	}

	void recur(int x, int y, int p) {
		int val = 0;
		if (x > y || y < x)
			return;
		if (x > 0) {
			if (p == 1) {
				val = arr[x] - arr[x - 1];
			}
			if (p == 3) {
				if (arr[x] - arr[x - 1] < K) {
					recur(x + 1, y, 3);
				} else
					val = arr[x] - arr[x - 1];
			}
		}
		if (y < N) {
			if (p == 4) {
				B += arr[y + 1] - arr[y];
			}
			if (p == 2) {
				if (arr[y + 1] - arr[y] < K) {
					recur(x, y - 1, 2);
				} else
					val = arr[y + 1] - arr[y];
			}
		}
		B += val;
		if (x == y) {
			System.out.println(B + " " + a);
			fa += B * a;
		}
		// System.out.println(Q);
		a *= Q;
		recur(x + 1, y, 1);
		recur(x, y - 1, 2);
		a /= Q;
		a *= (1 - Q);
		recur(x + 1, y, 3);
		recur(x, y - 1, 4);
		a /= (1 - Q);
		B -= val;
		// System.out.println(a+" "+B);
	}

	class cell implements Comparable<cell> {
		char ch;
		int i;

		cell(char c, int x) {
			ch = c;
			i = x;
		}

		public boolean equals(Object o) {
			cell other = (cell) o;
			return ((ch == other.ch && i == other.i));// || (v == other.u && u
														// ==
			// other.v));
		}

		@Override
		public int compareTo(cell c) {
			if (this.ch < c.ch)
				return -1;
			if (this.ch == c.ch) {
				if (this.i < c.i)
					return 1;
				if (this.i == c.i)
					return 0;
				return -1;
			}
			return 1;
		}

		public String toString() {
			return "[u=" + ch + ", v=" + i + "]";
		}

	}

	int T[] = new int[100010], L[] = new int[100010];
	int P[][] = new int[100010][30];

	void process3(int N) {
		int i, j;

		// we initialize every element in P with -1
		for (i = 0; i < N; i++)
			for (j = 0; 1 << j < N; j++)
				P[start[i]][j] = -1;

		// the first ancestor of every node i is T[i]
		for (i = 0; i < N; i++)
			P[start[i]][0] = T[i];

		// bottom up dynamic programing
		for (j = 1; 1 << j < N; j++)
			for (i = 0; i < N; i++)
				if (P[start[i]][j - 1] != -1)
					P[start[i]][j] = P[P[start[i]][j - 1]][j - 1];
	}

	int query(int p, int q) {
		int tmp = 0, log = 0, i = 0;

		// if p is situated on a higher level than q then we swap them
		if (L[p] < L[q])
			tmp = p;
		p = q;
		q = tmp;

		// we compute the value of [log(L[p)]
		for (log = 1; 1 << log <= L[p]; log++)
			;
		log--;

		// we find the ancestor of node p situated on the same level
		// with q using the values in P
		for (i = log; i >= 0; i--)
			if (L[p] - (1 << i) >= L[q])
				p = P[p][i];

		if (p == q)
			return p;

		// we compute LCA(p, q) using the values in P
		for (i = log; i >= 0; i--)
			if (P[p][i] != -1 && P[p][i] != P[q][i])
				p = P[p][i];
		q = P[q][i];

		return T[p];
	}

	long ans = 0;

	void recur(int i, int k, long sum) {
		if (k > K)
			return;
		if (k == K) {
			ans = Math.max(ans, sum);
		}
		for (int j = i; j < N; j++) {

			recur(j + 1, k + 1, sum);
		}
	}

	long[] mul(long arr[][], long temp[]) {
		long ans[] = new long[temp.length];
		for (int i = 0; i < arr.length; i++) {
			long sum = 0;
			for (int j = 0; j < arr.length; j++) {
				sum = (sum + arr[i][j] * temp[j]) % MOD;
			}
			ans[i] = sum;
		}
		return ans;
	}

	void printMat(long arr[][]) {
		for (int i = 0; i < arr.length; i++) {
			for (int j = 0; j < arr.length; j++) {
				System.out.print(arr[i][j] + " ");
			}
			System.out.println();
		}
		System.out.println("-----");
	}

	void printMat(long arr[]) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		System.out.println("-----");
	}

	long[][] matMul(int n, long arr[][], long y) {
		long iden[][] = new long[n][n];
		for (int i = 0; i < n; i++)
			iden[i][i] = 1;
		// printMat(iden);
		while (y > 0) {
			if (y % 2 == 1) {
				iden = mul(n, iden, arr);
				// printMat(iden);
				y--;
			} else {
				arr = mul(n, arr, arr);
				// printMat(arr);
				y /= 2;
			}
		}
		return iden;
	}

	long[][] mul(int n, long a1[][], long a2[][]) {
		long temp[][] = new long[n][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				long sum = 0;
				for (int k = 0; k < n; k++) {
					sum = (sum + a1[i][k] * a2[k][j]) % MOD;
				}
				temp[i][j] = sum;
			}
		}
		return temp;
	}

	void seive(int n) {
		b = new boolean[n + 1];
		prime = new int[n + 1];
		for (int i = 2; i * i <= n; i++) {
			if (!b[i]) {
				for (int j = 2 * i; j <= n; j += i) {
					if (!b[j]) {
						b[j] = true;
						prime[j] = i;
					}
				}
			}
		}
	}

	int binarySearch1(int arr[], int x) {
		int ans = -1;
		int low = 0, high = arr.length - 1;
		while (high >= low) {
			int mid = (low + high) / 2;
			if (arr[mid] >= x) {
				ans = mid;
				high = mid - 1;
			} else
				low = mid + 1;
		}
		return ans;
	}

	int binarySearch2(Integer arr[], int x) {
		int ans = -1;
		int low = 0, high = arr.length - 1;
		while (high >= low) {
			int mid = (low + high) / 2;
			if (arr[mid] >= x) {
				ans = mid;
				low = mid + 1;
			} else
				high = mid - 1;
		}
		return ans + 1;
	}

	int cntEven(String str) {
		int cnt = 0;
		for (int i = str.length() - 1; i >= 0; i--) {
			if ((str.charAt(i) - '0') % 2 == 0) {
				cnt++;
			}
		}
		return cnt;
	}

	int max = 0;

	int getParent(int x) {
		// System.out.println(x+" "+parent[x]);
		if (parent[x] != x) {
			parent[x] = getParent(parent[x]);
		}
		return parent[x];
	}

	class Pair implements Comparable<Pair> {
		int u;
		int v, r, i;

		Pair(int u, int v, int r, int i) {
			this.u = u;
			this.v = v;
			this.r = r;
			this.i = i;
		}

		Pair(int u, int v, int r) {
			this.u = u;
			this.v = v;
			this.r = r;
		}

		Pair(int u, int v) {
			this.u = u;
			this.v = v;
		}

		public int hashCode() {
			return Objects.hash();
		}

		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));// || (v == other.u && u ==
			// other.v));
		}

		public int compareTo(Pair other) {
			// return Long.compare(r, other.r);
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u))
					: (Long.compare(v, other.v));
			// :(Long.compare(other.r, r))) ;
		}

	}

	int min(int x, int y) {
		if (x < y)
			return x;
		return y;
	}

	int max(int x, int y) {
		if (x > y)
			return x;
		return y;
	}

	long modInverse(long a, long mOD2) {
		return power(a, mOD2 - 2, mOD2);
	}

	long power(long x, long y, long m) {
		if (y == 0)
			return 1;
		long p = power(x, y / 2, m) % m;
		p = (p * p) % m;

		return (y % 2 == 0) ? p : (x * p) % m;
	}

	boolean isPrime(int x) {
		for (int i = 2; i * 1L * i <= x; i++)
			if (x % i == 0)
				return false;
		return true;
	}

	public long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	void failFn(String str, int arr[]) {
		int len = 0;
		arr[0] = 0;
		int i = 1;
		while (i < arr.length) {
			if (str.charAt(i) == str.charAt(len)) {
				arr[i++] = ++len;
				continue;
			}
			if (len == 0) {
				arr[i] = len;
				i++;
				continue;
			}
			if (str.charAt(i) != str.charAt(len)) {
				len = arr[len - 1];
			}
		}
	}

	static class ST1 {
		int arr[], st[], size;

		ST1(int a[]) {
			arr = a.clone();
			size = 10 * arr.length;
			st = new int[size];
			build(0, arr.length - 1, 1);
		}

		void build(int ss, int se, int si) {
			if (ss == se) {
				st[si] = arr[ss];
				return;
			}
			int mid = (ss + se) / 2;
			int val = 2 * si;
			build(ss, mid, val);
			build(mid + 1, se, val + 1);
			st[si] = (st[val] + st[val + 1]);
		}

		int get(int ss, int se, int l, int r, int si) {
			if (l > se || r < ss || l > r)
				return Integer.MAX_VALUE;
			if (l <= ss && r >= se)
				return st[si];
			int mid = (ss + se) / 2;
			int val = 2 * si;
			return (get(ss, mid, l, r, val) + get(mid + 1, se, l, r, val + 1));
		}
	}

	static class ST {
		int arr[], lazy[], n;

		ST(int a) {
			n = a;
			arr = new int[10 * n];
			lazy = new int[10 * n];
		}

		void up(int l, int r, int val) {
			update(0, n - 1, 0, l, r, val);
		}

		void update(int l, int r, int c, int x, int y, int val) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] ^= lazy[c];
				lazy[2 * c + 2] ^= lazy[c];
				if (l == r)
					arr[c] ^= lazy[c];
				lazy[c] = 0;
			}
			if (l > r || x > y || l > y || x > r)
				return;
			if (x <= l && y >= r) {
				if ((r - l + 1) % 2 == 1)
					lazy[c] ^= val;
				return;
			}
			int mid = l + r >> 1;
			update(l, mid, 2 * c + 1, x, y, val);
			update(mid + 1, r, 2 * c + 2, x, y, val);
			arr[c] = (arr[2 * c + 1] + arr[2 * c + 2]);
		}

		int an(int ind) {
			return ans(0, n - 1, 0, ind);
		}

		int ans(int l, int r, int c, int ind) {
			if (lazy[c] != 0) {
				lazy[2 * c + 1] += lazy[c];
				lazy[2 * c + 2] += lazy[c];
				if (l == r)
					arr[c] += lazy[c];
				lazy[c] = 0;
			}
			if (l == r)
				return arr[c];
			int mid = l + r >> 1;
			if (mid >= ind)
				return ans(l, mid, 2 * c + 1, ind);
			return ans(mid + 1, r, 2 * c + 2, ind);
		}
	}

	static long[] array;

	public static class FenwickTree {

		// 1-indexed array, In this array We save cumulative
		// information to perform efficient range queries and
		// updates

		public FenwickTree(int size) {
			array = new long[size + 1];
		}

		int getSum(int index) {
			int sum = 0; // Iniialize result

			// index in BITree[] is 1 more than the index in arr[]
			index = index + 1;

			// Traverse ancestors of BITree[index]
			while (index > 0) {
				// Add current element of BITree to sum
				sum ^= array[index];

				// Move index to parent node in getSum View
				index -= index & (-index);
			}
			return sum;
		}

		public long rsq(int ind) {
			assert ind > 0;
			long sum = 0;
			ind = ind + 1;
			while (ind > 0) {
				sum ^= array[ind];
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and decrementing ind by that
				// number
				ind -= ind & (-ind);
			}
			return sum;
		}

		public long rsq(int a, int b) {
			assert b >= a && a > 0 && b > 0;
			return rsq(b) ^ rsq(a - 1);
		}

		public void update(int ind, long value) {
			assert ind > 0;
			ind = ind + 1;
			while (ind < array.length) {
				array[ind] ^= value;
				// Extracting the portion up to the first significant one of the
				// binary representation of 'ind' and incrementing ind by that
				// number
				ind += ind & (-ind);
			}
		}

		public int size() {
			return array.length - 1;
		}
	}

	public static int[] shuffle(int[] a, Random gen) {
		for (int i = 0, n = a.length; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int d = a[i];
			a[i] = a[ind];
			a[ind] = d;
		}
		return a;
	}

	long power(long x, long y, int mod) {
		long ans = 1;
		while (y > 0) {
			if (y % 2 == 0) {
				x = (x * x) % mod;
				y /= 2;
			} else {
				ans = (x * ans) % mod;
				y--;
			}
		}
		return ans;
	}

	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		out.close();
		out.flush();
		tr(System.currentTimeMillis() - s + "ms");
	}

	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}

	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
			// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}