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 Python (3.4.3) (judge verdict: Wrong Answer)

#import decimal
#decimal.getcontext().prec==500 Floatの桁数を500まで増やす
#Decimal(c).sqrt() それで平方根を求める
#Decimal(1) / Decimal(7) 1/7

from collections import *
from itertools import *
from bisect import *
from heapq import *
import copy
import math
from fractions import gcd
import sys
#input = sys.stdin.readline

N,M=map(int,input().split())
A=list(map(int,input().split()))

data=[]
for i,a in enumerate([2,5,5,4,5,6,3,7,6]):
    if i+1 in A:
        data.append([a,i+1])

dic={}
for a,i in reversed(data):
    dic[i]=0
dp=[copy.copy(dic) for i in range(N+1)]

def main(dic1,dic2):
    dic1=sorted([[str(i),dic1[i]] for i in dic],key=lambda x:x[0],reverse=True)
    dic2=sorted([[str(i),dic2[i]] for i in dic],key=lambda x:x[0],reverse=True)
    for a,b in zip(dic1,dic2):
        if a[1]>b[1]:
            return(0)
        if a[1]<b[1]:
            return(1)
    return(0)

def _sum(dic):
    count=0
    for i in dic:
        count+=dic[i]
    return(count)


for a,n in data:
    tempdic=copy.copy(dic)
    tempdic[n]+=1
    if i>=a:
        flag=main(dp[a],tempdic)
        if flag:
            dp[a]=tempdic
    for i in range(len(dp)):
        if i>=a and _sum(dp[i-a]):
            if _sum(dp[i])<_sum(dp[i-a])+1:

                tempdic=copy.copy(dp[i-a])
                tempdic[n]+=1
                dp[i]=tempdic
            elif _sum(dp[i])==_sum(dp[i-a])+1:
                dp[i-a][n]+=1
                flag=main(dp[i],dp[i-a])
                dp[i-a][n]-=1
                if flag:
                    tempdic=copy.copy(dp[i-a])
                    tempdic[n]+=1
                    dp[i]=tempdic
dic=dp[N]
a=""
dic=sorted([[str(i),dic[i]] for i in dic],key=lambda x:x[0],reverse=True)
for i,z in dic:
    for m in range(z):
        a+=i
print(a)