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: Runtime Error)

from collections import defaultdict
N, _ = map(int, input().split())
A = list(map(int, input().split()))
table = defaultdict(int)
for i, cost in zip(range(1, 10), [2,5,5,4,5,6,3,7,6]):
    if i in A:
        table[cost] = max(table[cost], i)
candy = sorted(table)
res = defaultdict(int)
for k in range(len(candy)):
    bits = 1
    for i in candy[k + 1:]:
        bits = bits | (bits << i)
    for i in range(1, len(format(bits, 'b'))):
        if bits & (1 << i):
            if N - i >= 0 and (N - i) % candy[k] == 0:
                res[table[candy[k]]] = ((N - i) // candy[k])
                N = i
                break
    if N == candy[k]:
        res[table[candy[k]]] = 1
        N = 0
#swap
for _ in range(2):
    for candy1 in candy:
        for candy2 in candy:
            for candya in candy:
                sum1 = candy1 + candy2 + candya
                for candy3 in candy:
                    for candy4 in candy:
                        for candyb in candy:
                            sum2 = candy3 + candy4 + candyb
                            if sum1 == sum2:
                                x = sorted([table[candy1], table[candy2], table[candya]], reverse=True)
                                y = sorted([table[candy3], table[candy4], table[candyb]], reverse=True)
                                if x < y:
                                    a, b, ab = x
                                    c, d, cd = y
                                    t = min(res[a], res[b], res[ab])
                                    if len({res[a], res[b], res[ab]}) == 1:
                                        t = res[a] // 3
                                    elif res[a] == res[b]:
                                        t = min(res[a] // 2, res[c])
                                    elif res[b] == res[c]:
                                        t = min(res[a], res[c]//2)
                                    elif res[c] == res[a]:
                                        t = min(res[a]//2, res[b])
                                    res[a] -= t
                                    res[b] -= t
                                    res[ab] -= t
                                    res[c] += t
                                    res[d] += t
                                    res[cd] += t
for _ in range(2):
    for candy1 in candy:
        for candy2 in candy:
            sum1 = candy1 + candy2
            for candy3 in candy:
                for candy4 in candy:
                    sum2 = candy3 + candy4
                    if sum1 == sum2:
                        x = sorted([table[candy1], table[candy2]], reverse=True)
                        y = sorted([table[candy3], table[candy4]], reverse=True)
                        if x < y:
                            a, b = x
                            c, d = y
                            t = min(res[a], res[b])
                            if res[a] == res[b]:
                                t = res[a] // 2
                            res[a] -= t
                            res[b] -= t
                            res[c] += t
                            res[d] += t
tmp = []
for i, d in res.items():
    tmp += [i] * d
print(''.join(map(str, sorted(tmp, reverse=True))))