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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <fstream>
#include <iostream>
#include <algorithm>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <sstream>
#include <map>
#include <set>
#include <vector>
#include <cmath>
#include <queue>
#include <random>

using namespace std;

#define INT_MAX_VALUE 2147483647
#define LONG_LONG_MAX_VALUE 9223372036854775807

template <class T>
T mmax(T a,T b){
    if(a>=b){
        return a;
    }
    return b;
}
template <class T>
T mmin(T a,T b){
    if(a<=b){
        return a;
    }
    return b;
}

long long gcd(long long a, long long b){
    if(a<b){
        swap(a,b);
    }
    while(b){
        long long r = a%b;
        a=b;
        b=r;
    }
    return a;
}

long long lcm(long long a, long long b){
    return (a*b)/gcd(a,b);
}

int isPrim(int a){
    if(a==1){
        return 0;
    }
    for(int i=2;i<=(a+1)/2;i++){
        if(a%i==0){
            return 0;
        }
    }
    return 1;
}

long long mod_pow(long long x, long long n, long long mod){
    //xのn乗を計算するのにn乗を2進表記にして計算
    //x^22 = x^16 + x^4 + x^2
    long long ret=1;
    while(n>0){
        if(n&1){
            ret=(ret*x)%mod;//答えに付加
        }
        x=(x*x)%mod;//2乗
        n >>=1;
    }
    return ret;
}


struct XX{
    int cnt;
    int x;
    int y;
};


class xxGreater {
public:
    bool operator()(const XX& riLeft, const XX& riRight) const {
        //第2条件
        if((riLeft.x) == (riRight.x)){
            return riLeft.y > riRight.y;//<:昇順(小さいものから順番)、>:降順(大きいものから順番)
        }
        //第1条件
        return (riLeft.x) > (riRight.x);
    }
};


//union-find
//int ppar[100001];
//int rrank[100001];
//
//void init(int n){
//    for(int i=0;i<n;i++){
//        ppar[i]=i;
//        rrank[i]=0;
//    }
//}
//
//int find(int x){
//    if(ppar[x]==x){
//        return x;
//    }else{
//        return ppar[x]=find(ppar[x]);
//    }
//}
//
//void unite(int x,int y){
//    x=find(x);
//    y=find(y);
//    if(x==y){
//        return;
//    }
//    if(rrank[x]<rrank[y]){
//        ppar[x]=y;
//    }else{
//        ppar[y]=x;
//        if(rrank[x]==rrank[y]){
//            rrank[x]++;
//        }
//    }
//}
//bool same(int x,int y){
//    return find(x)==find(y);
//}
//
////kruskal
//struct edge{
//    int u;
//    int v;
//    int cost;
//};
//
//bool comp(edge& e1,edge& e2){
//    return e1.cost < e2.cost;
//}
//
//edge es[200000];
//
//long long kruskal(int V,int E){//V:頂点数,E:辺数
//    sort(es,es+E,comp);
//    init(V);
//    long long res = 0;
//    for(int i=0;i<E;i++){
//        edge e = es[i];
//        if(!same(e.u,e.v)){
//            unite(e.u,e.v);
//            res+=e.cost;
//        }
//    }
//    return res;
//}



int main(int argc, const char * argv[])
{
    //std::ios::sync_with_stdio(false);
    //scanf("%s",S);
    //scanf("%d",&N);
    //sscanf(tmp.c_str(),"%dd%d%d",&time[i], &dice[i], &z[i]);
    //getline(cin, target);
    //cin >> x >> y;
    //テスト用
    //ifstream ifs( "1_06.txt" );
    //ifs >> a;
    //ここから
    
    long long N,k;
    cin >> N >> k;
    long long a[100000];
    for(int i=0;i<N;i++){
        cin >> a[i];
    }
    
    sort(a,a+N);
    long long mingcd=2000000000;
    for(int i=1;i<N;i++){
        if(mingcd>gcd(a[0],a[i])){
            mingcd=gcd(a[0],a[i]);
        }
    }
    if(mingcd==1){
        cout << "POSSIBLE" << endl;
    }else{
        cout << "IMPOSSIBLE" << endl;
    }
    
    //cout << ans << endl;
    
    //ここまで
    //cout << "ans" << endl;改行含む
    //printf("%.0f\n",ans);//小数点以下表示なし
    //printf("%.7f\n",p);
    //printf("%f\n",pow(2,ans.size()));
    
    return 0;
}