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<string>
#include<algorithm>
using namespace std;
static const int MAX_N=10e4;
int num[9]={2,5,5,4,5,6,3,7,6};
int a[9];
int dp[10][MAX_N];
int main(void){
	int N,M;
		cin >> N >> M;
	for(int i=0;i<M;i++)
		cin >> a[i];
	for(int i=1;i<=N;i++)
		dp[0][i]=-1;
	sort(a,a+M);

	
	
	
	for(int i=0;i<M;i++){
		for(int j=1;j<=N;j++){
			if(j-num[a[i]-1]<0 || dp[i+1][j-num[a[i]-1]]==-1)
				dp[i+1][j]=dp[i][j];
			else if(dp[i+1][j-num[a[i]-1]]+1>dp[i][j])
				dp[i+1][j]=dp[i+1][j-num[a[i]-1]]+1;
			else
				dp[i+1][j]=dp[i][j];
		}
	}
	
	int i=M,j=N;
	while(dp[i][j]>0){
		if(j-num[a[i-1]-1]<0 || dp[i][j-num[a[i-1]-1]]==-1)
			i--;
		else if(dp[i][j]==dp[i][j-num[a[i-1]-1]]+1){
			cout << a[i-1];
			j-=(num[a[i-1]-1]);
		}
		else
			i--;
	}
	cout << endl;
	
	
	return 0;
}