Problem: Diana loves playing with numbers. She's got n cards with positive integer numbers a_i written on them. She spends her free time multiplying the numbers on the cards. She picks a non-empty subset of the cards and multiplies all the numbers a_i written on them.

Diana is happy when the product of the numbers ends with her favorite digit d. Now she is curious what cards she should pick so that the product of the numbers on them is the largest possible and the last decimal digit of the product is d. Please, help her.

Input

The first line contains the integers n and d (1≤ n≤ 10^5, 0≤ d≤ 9). The second line contains n integers a_i (1≤ a_i≤ 1000). 

Output

On the first line, print the number of chosen cards k (1≤ k≤ n). On the next line, print the numbers written on the chosen cards in any order. 

If it is impossible to choose a subset of cards with the product that ends with the digit d, print the single line with -1.

Examples

Input


6 4
4 11 8 2 1 13


Output


5
1 2 4 11 13 


Input


3 1
2 4 6


Output


-1


Input


5 7
1 3 1 5 3


Output


-1


Input


6 3
8 9 4 17 11 5


Output


3
9 11 17 


Input


5 6
2 2 2 2 2


Output


4
2 2 2 2 

Note

In the first example, 1 × 2 × 4 × 11 × 13 = 1144, which is the largest product that ends with the digit 4. The same set of cards without the number 1 is also a valid answer, as well as a set of 8, 11, and 13 with or without 1 that also has the product of 1144.

In the second example, all the numbers on the cards are even and their product cannot end with an odd digit 1.

In the third example, the only possible products are 1, 3, 5, 9, 15, and 45, none of which end with the digit 7.

In the fourth example, 9 × 11 × 17 = 1683, which ends with the digit 3. 

In the fifth example, 2 × 2 × 2 × 2 = 16, which ends with the digit 6.

Solution (in CPP):

Solution:
// #undef _GLIBCXX_DEBUG

#include <bits/stdc++.h>
using namespace std;
 
#ifdef SG
	#include <debug.h>
#else
	#define show(...)
	#define debug(...)
	#define deepen(...)
	#define timer(...)
#endif
 
#define ARG4(_1,_2,_3,_4,...) _4
 
#define forn3(i,l,r) for (int i = int(l); i < int(r); ++i)
#define forn2(i,n) forn3 (i, 0, n)
#define forn(...) ARG4(__VA_ARGS__, forn3, forn2) (__VA_ARGS__)
 
#define ford3(i,l,r) for (int i = int(r) - 1; i >= int(l); --i)
#define ford2(i,n) ford3 (i, 0, n)
#define ford(...) ARG4(__VA_ARGS__, ford3, ford2) (__VA_ARGS__)
 
#define forv(i,v) for (auto i = v.begin(); i != v.end(); ++i)
#define forr(i,v) for (auto i = v.end(); i != v.begin() && (--i, 1); )
#define ve vector
#define pa pair
#define tu tuple
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define fs first
#define sc second
#define all(a) (a).begin(), (a).end()
#define sz(a) ((int)(a).size())
 
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int ui;
typedef unsigned char uc;
typedef pa<int, int> pii;
typedef pa<int, ll> pil;
typedef pa<ll, int> pli;
typedef pa<ll, ll> pll;
typedef ve<int> vi;
 
const ld pi = 3.1415926535897932384626433832795l;
 
template<typename T> inline auto sqr (T x) -> decltype(x * x) {return x * x;}
template<typename T> inline T abs (T x) {return x > T() ? x : -x;}
template<typename T1, typename T2> inline bool umx (T1& a, T2 b) {if (a < b) {a = b; return 1;} return 0;}
template<typename T1, typename T2> inline bool umn (T1& a, T2 b) {if (b < a) {a = b; return 1;} return 0;}
 
const int period[10] = {1, 1, 4, 4, 2, 1, 1, 4, 4, 2};
vi pw[10];
vi a[10];
ve<pa<pii, ld> > t[10];
int d;

ld best;
vi ans;
vi ord;

void calc(int i, int curd, ld curc) {
	if (i == 10) {
		if (curd == d && umn(best, curc)) {
			ans = ord;			
		}
		return;
	}
	forn(j, sz(t[i])) {
		ord.pb(t[i][j].fs.sc);
		calc(i + 1, (curd * t[i][j].fs.fs) % 10, curc + t[i][j].sc);
		ord.pop_back();
	}
}

int main () {
	std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
	cout.setf(ios::showpoint | ios::fixed);
	cout.precision(20);
#ifdef SG
	freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);
#endif
	forn(i, 10) {
		pw[i].resize(4);
		pw[i][0] = i;
		forn(j, 1, 4) {
			pw[i][j] = (pw[i][j - 1] * i) % 10;
		}
	}
	int n;
	cin >> n >> d;
	forn(i, n) {
		int b;
		cin >> b;
		a[b % 10].pb(b);
	}
	forn(i, 10) {
		sort(all(a[i]));
	}             
	debug(a, a + 10);
	forn(i, 10) {		
		ld cur = 0;
		forn(j, sz(a[i])) {
			cur += logl(a[i][j]);					
		}
		t[i].pb(mp(mp(1, sz(a[i])), cur));
		forn(j, min(4, sz(a[i]))) {
			ld cost = 0;
			forn(k, j) {
				cost += logl(a[i][k]);
			}
			t[i].pb(mp(mp(pw[i][(sz(a[i]) - j - 1) % 4], j), cost));
		}
	}
	best = 1e9;
	debug(t, t + 10);
	calc(0, 1, 0l);
	if (best > 1e8) {
		cout << -1 << "\n";
		return 0;
	}
	vi res;
	forn(i, 10) {
		forn(j, ans[i], sz(a[i])) {
			res.pb(a[i][j]);
		}
	}
	if (sz(res) == 0) {
		cout << "-1\n";
		return 0;
	}
	cout << sz(res) << endl;
	forn(i, sz(res)) {
		cout << res[i] << " ";
	}
	cout << endl;
	return 0;
}