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: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int MAX = 1e4 + 9;
int digit[11] = {2, 5, 5, 4, 5, 6, 3, 7, 6}, dp[MAX], n, m, a[11];

int main() {
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);

	cin >> n >> m;
	for (int i = 0; i < m; i++) {
		cin >> a[i]; 
		a[i]--;
	}
	sort(a, a + m, greater<int>());
	dp[0] = 1;
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j < m; j++) {
			if (i - digit[a[j]] < 0) continue;
			if (dp[i - digit[a[j]]] > 0) dp[i] = max(dp[i], dp[i - digit[a[j]]] + 1);
		}
	}
	int len = dp[n];
	while (n) {
		for (int i = 0; i < m; i++) {
			if (n - digit[a[i]] < 0) continue;
			if (dp[n - digit[a[i]]] == len - 1) {
				cout << (char)(a[i] + 1 + '0');
				n -= digit[a[i]];
				len--;
				break;
			}
		}
	}
	
	return 0;
}