// Smile please :)

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cassert>
#include <cctype>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <string>
#include <iomanip>
#include <numeric>
#include <vector>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <list>
#include <bitset>
#include <climits>
#include <unordered_map>
#include <unordered_set>
using namespace std;

//#undef KVARK_DEBUG

#ifdef KVARK
#define dbg(x) cout << #x << " = " << (x) << endl;
#define dbg2(a, b) cout << #a << " = " << (a) << "; " \
                        << #b << " = " << (b) << endl;
#define dbg3(a, b, c) cout << #a << " = " << (a) << "; " \
                           << #b << " = " << (b) << "; " \
                           << #c << " = " << (c) << endl;
#define dbg4(a, b, c, d) cout << #a << " = " << (a) << "; " \
                              << #b << " = " << (b) << "; " \
                              << #c << " = " << (c) << "; " \
                              << #d << " = " << (d) << endl;
#define dbg5(a, b, c, d, e) cout << #a << " = " << (a) << "; " \
                                 << #b << " = " << (b) << "; " \
                                 << #c << " = " << (c) << "; " \
                                 << #d << " = " << (d) << "; " \
                                 << #e << " = " << (e) << endl;
#define dbgp(a) cout << #a << " = {" << (a).first << ", " << (a).second << "}" << endl;
#else
#define dbg(...) (void(1));
#define dbg2(...) (void(1));
#define dbg3(...) (void(1));
#define dbg4(...) (void(1));
#define dbg5(...) (void(1));
#define dbgp(...) (void(1));
#endif

typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<double, int> pdi;
typedef vector<int> vi;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vector<int> > vvi;
typedef vector<vector<pii> > vvpii;
typedef vector<vector<long long> > vvl;
typedef vector<long long> vl;
typedef long long int llint;
#define ALL(v) (v.begin()), (v.end())
#define SZ(v) ((int)((v).size()))
#define endl "\n"
class LCMGCD {
public:
    string isPossible(vector <int> x, int t);
};

const int INF = 0x3f3f3f3f;
const int N = 3e5+10;
const int M = 3e5+10;



string LCMGCD::isPossible(vector <int> x, int t) {
    srand(time(0));
    auto s = clock();
    vpii v;

    while ((double)( clock() - s) / CLOCKS_PER_SEC < 1.5) {
        random_shuffle(ALL(x));
        set<llint> st[2];
        st[1].insert(x[0]);
        for (int i = 1; i < x.size(); ++i) {
            int cur = i % 2;
            int next = (i + 1) % 2;
            st[next].clear();
            for (llint p: st[cur]) {
                if ((double)( clock() - s) / CLOCKS_PER_SEC > 1.8)
                    return "Impossible";
                st[next].insert(__gcd((llint)x[i], p));
                if ((double)( clock() - s) / CLOCKS_PER_SEC > 1.8)
                    return "Impossible";
                st[next].insert(x[i] / __gcd((llint)x[i], p) * p);
                if ((double)( clock() - s) / CLOCKS_PER_SEC > 1.8)
                    return "Impossible";
            }
        }
        int last = x.size() % 2;
        if (st[last].count(t))
            return "Possible";
    }
    return "Impossible";
}

<%:testing-code%>
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