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 sys

def chk(i,j):
    tmp=[p[i][k] for k in range(M)]
    tmp[j]=p[i][j]+1
    for k in range(M-1,-1,-1):
        if tmp[k] > p[i+x[j]][k] :
            p[i+x[j]]=[tmp[k] for k in range(M)]

N,M=map(int,input().split())
x=[0,2,5,5,4,5,6,3,7,6]
a=list(map(int,input().split()))
a.sort()
b=[]
for i in range(M):
    for j in range(M):
        if x[a[j]]==x[a[i]]: tmp=j
    b.append(a[tmp]) 

a=list(set(b))
a.sort()
M=len(a)
x=[ x[a[i]] for i in range(M) ]
print("a:",a)
print("x:",x)


p=[-100 for i in range(N+10)]
p[0]=0
for i in range(N):
    if p[i]>-1:
        for j in range(M):
            p[i+x[j]]=max(p[i+x[j]],p[i]+1)

ans=""
while N>0:
    for j in range(M-1,-1,-1):
        if p[N]==p[N-x[j]]+1:
            ans+=str(a[j])
            N-=x[j]
            break
print(ans)