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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;

vi mts={0,2,5,5,4,5,6,3,7,6};

void solve(int N, int M, vi& A){
  vi u(8,-1);
  for (int i=0;i<M;++i){
    int m=mts[A[i]];
    u[m]=max(u[m],A[i]);
  }

  vvi dp(N+10, vi(10,-1));
  for (int i=0;i<N;++i){
    for (int m=2;m<=7;++m){
      int p=10-u[m];
      if(p==-1){continue;}
      dp[i][p]++;
      dp[i][0]++;
      dp[i+m]=max(dp[i+m], dp[i]);
      dp[i][p]--;
      dp[i][0]--;
    }
  }

  for (int n=9;n>=1;--n){
    for (int j=0;j<dp[N][10-n];++j){
      putchar('0'+n);
    }
  }
  putchar('\n');
}

int main(){
  int N,M;cin>>N>>M;
  vi A;
  for (int i=0;i<M;++i){
    cin>> A[i];
  }
  solve(N, M, A);
  return 0;
}