Problem:
Score : 400 points

Problem Statement

Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:

Every digit in the integer must be one of the digits A_1, A_2, ..., A_M (1 \leq A_i \leq 9).

The number of matchsticks used to form digits 1, 2, 3, 4, 5, 6, 7, 8, 9 should be 2, 5, 5, 4, 5, 6, 3, 7, 6, respectively.

Constraints

All values in input are integers.

2 \leq N \leq 10^4

1 \leq M \leq 9

1 \leq A_i \leq 9

A_i are all different.

There exists an integer that can be formed by exactly N matchsticks under the conditions.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M

Output

Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.

Sample Input 1

20 4
3 7 8 4

Sample Output 1

777773

The integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.

Sample Input 2

101 9
9 8 7 6 5 4 3 2 1

Sample Output 2

71111111111111111111111111111111111111111111111111

The output may not fit into a 64-bit integer type.

Sample Input 3

15 3
5 4 6

Sample Output 3

654

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define INF (1LL << 60)
typedef long long LL;
using namespace std;

int main() {
	int num[10] = {10, 2, 5, 5, 4, 5, 6, 3, 7, 6 };
	int n, m;	cin >> n >> m;
	vector<int> a(m);
	for (auto &x : a) {
		cin >> x;
	}

	vector<LL> dp(n + 1, -INF);
	dp[0] = 0;
	for (int i = 1; i <= n; i++) {
		for (auto x : a) {
			if (i < num[x]) continue;
			dp[i] = max(dp[i], dp[i - num[x]] + 1);
		}
	}
	
	sort(a.begin(), a.end(), std::greater<int>());

	LL match = n;
	LL ans = 0;
	while (match > 0) {
		for (auto x : a) {
			if (match < num[x]) continue;
			if (dp[match - num[x]] == dp[match] - 1) {
				ans += pow(10, dp[match] - 1) * x;
				match -= num[x];
				break;
			}
		}
	}
	cout << ans;
}