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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program atcoder
    implicit none
    integer(8) :: i,j,n,m,ans=0,k,mincost=-1,use2max=-1
    integer(8),allocatable,dimension(:) :: a,canuse,cost
    character(len=10000),allocatable,dimension(:) :: dp,x
    read*,n,m
    allocate(a(m))
    allocate(canuse(9))
    allocate(cost(9))
    allocate(dp(0:n))
    dp = "-"
    x = (/"1","2","3","4","5","6","7","8","9"/);
    cost = (/2,5,5,4,5,6,3,7,6/)
    read(*,*)(a(j),j=1,m)
    dp(0) = ""
    do i=0,N
        if(trim(dp(i))=="-")then
            cycle
        endif
        do j=1,m
            if(i+cost(a(j)) > N )then
                cycle
            endif
           dp(i+cost(a(j))) = maxst( dp(i+cost(a(j))) , trim(dp(i))//x(a(j)) )
        enddo
    enddo
    write(*,'(a)')trim(dp(n))
    stop 
contains
function maxst(x,y)
    character maxst*10000,x*10000,y*10000
    if(x=="-")then
        maxst = y
    else if(y=="-")then
        maxst = x
    else if(len(trim(x))>len(trim(y)))then
        maxst = x
    else if(len(trim(x))<len(trim(y)))then
        maxst = y
    else if(x>=y)then
        maxst = x
    else
        maxst = y
    endif
end function maxst
end program atcoder