Problem:
Score : 300 points

Problem Statement

Iroha is very particular about numbers. There are K digits that she dislikes: D_1, D_2, ..., D_K.

She is shopping, and now paying at the cashier.
Her total is N yen (the currency of Japan), thus she has to hand at least N yen to the cashier (and possibly receive the change).

However, as mentioned before, she is very particular about numbers. When she hands money to the cashier, the decimal notation of the amount must not contain any digits that she dislikes. Under this condition, she will hand the minimum amount of money.

Find the amount of money that she will hand to the cashier.

Constraints

1 ≦ N < 10000

1 ≦ K < 10

0 ≦ D_1 < D_2 < … < D_K≦9

\{D_1,D_2,...,D_K\} ≠ \{1,2,3,4,5,6,7,8,9\}

Input

The input is given from Standard Input in the following format:

N K
D_1 D_2 … D_K

Output

Print the amount of money that Iroha will hand to the cashier.

Sample Input 1

1000 8
1 3 4 5 6 7 8 9

Sample Output 1

2000

She dislikes all digits except 0 and 2.

The smallest integer equal to or greater than N=1000 whose decimal notation contains only 0 and 2, is 2000.

Sample Input 2

9999 1
0

Sample Output 2

9999

Solution in Ruby (2.7.1) (judge verdict: Accepted)

N,k=gets.chomp.split(" ")
N_i = N.to_i
K = k.to_i
d_array=gets.chomp.split(" ").map(&:to_i)
E_array= (0..9).to_a - d_array

if 10-K == 1
    ret = E_array[0]
    while ret < N_i
        ret = ret*10 + E_array[0]
    end
    puts ret
    exit
end

# 使える数字を元にn進数を10進数にする
def to_i10(n)
    n_s = n.to_s(10-K)
    ret = 0

    start = 0
    diff = 0
    if E_array[0]!=0 && n_s.length>1
        if n_s[0]=="1" && n_s[1]=="0"
	        diff = E_array[-1] - E_array[0]
        else
            ret = E_array[n_s[0].to_i-1]
            diff = -1 if n_s.length==2 
        end
        start=1
    end

    (start..(n_s.length-1)).each do |i|
        ret = ret*10 + E_array[n_s[i].to_i] + diff
        diff = 0
    end
    ret
end

sup = (10**N.length).to_s(10-K).to_i
inf = 0
loop do
    mid = (sup + inf)/2
    if inf == mid
        puts to_i10(sup)
        break
    end

    mid_i10 = to_i10(mid)
    if mid_i10 < N_i
        inf = mid
    else
        sup = mid
    end
end