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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>


unsigned long long *BALL_BOX;
int *CHECK_BOX;
unsigned long long MAX_RANGE;
int N;


/* 絶対値を逆算的に求める */
int Work(unsigned long long serch_num)
{
	unsigned long long bk;		// 一時的に格納
	int i, j;


	// フラグチェック、既に求めた値であれば終了する
	if(CHECK_BOX[serch_num] == 1)
		return 0;

	// 一度チェックした値にフラグを立てる
	CHECK_BOX[serch_num] = 1;

	// 元の配列にあるかチェック
	for(i = 0; i < N; i++){
		if(BALL_BOX[i] == serch_num){
			return 1;
		}
	}

	// 分岐処理(求めた値をさらに調べる、見つけれなければ次の処理へ)
	for(i = 0; i < N; i++){

		if(BALL_BOX[i] >= serch_num){
			bk = BALL_BOX[i] - serch_num;
			if(Work(bk) == 1)
				return 1;
		}

		bk = BALL_BOX[i] + serch_num;
		if(bk <= MAX_RANGE)
			if(Work(bk) == 1)
				return 1;
	}

	return 0;
}


int main()
{
	char in[20];
	char c;
	unsigned long long int K;
	int i;


	fgets(in, sizeof(in), stdin);
	sscanf(in, "%d %lld", &N, &K);

	BALL_BOX = (unsigned long long *)malloc(sizeof(unsigned long long) * N);

	i = MAX_RANGE = 0;
	while((c = fgetc(stdin)) && i < N){
		if(isdigit(c)){
			ungetc(c, stdin);
			scanf("%lld", &BALL_BOX[i]);
			if(BALL_BOX[i] > MAX_RANGE)
				MAX_RANGE = BALL_BOX[i];
			i++;
		}
	}


	// 求めようとする値が最大値を超えていれば不可
	if(K > MAX_RANGE){
		printf("IMPOSSIBLE\n");
		return 0;
	}

	// 初期化処理
	CHECK_BOX = (int *)malloc(sizeof(int) * MAX_RANGE + 1);
	for(i = 0; i <= MAX_RANGE; i++)
		CHECK_BOX[i] = 0;

	/*
	printf("MAX = %lld\n", MAX_RANGE);
	for(i = 0; i < MAX_RANGE + 1; i++){
		printf("%d ", CHECK_BOX[i]);
	}
	printf("\n");
	*/

	if(Work(K) == 1)
		printf("POSSIBLE\n");
	else
		printf("IMPOSSIBLE\n");

	return 0;
}