Problem:
Score : 500 points

Problem Statement

Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

Constraints

1 \leq N < 10^{100}

1 \leq K \leq 3

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the count.

Sample Input 1

100
1

Sample Output 1

19

The following 19 integers satisfy the condition:

1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

Sample Input 2

25
2

Sample Output 2

14

The following 14 integers satisfy the condition:

11,12,13,14,15,16,17,18,19,21,22,23,24,25

Sample Input 3

314159
2

Sample Output 3

937

Sample Input 4

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3

Sample Output 4

117879300

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

n = gets.chomp.chars
s = n.size
k = gets.to_i

ans = 0
(1..s).to_a.combination(k) do |arr|
    if arr[0] == 1
        if k != 1 && (arr[1] == 2 || n[1..(arr[1]-2)].all?{|e| e=="0"})
            if k != 2 && (arr[2] == arr[1]+1 || n[arr[1]..(arr[2]-2)].all?{|e| e=="0"})
                ans += (n[0].to_i-1) * 9 ** 2 + [(n[arr[1]-1].to_i-1),0].min * 9 + n[arr[2]-1].to_i
            else
                ans += (n[0].to_i-1) * 9 ** (k-1) + n[arr[1]-1].to_i.min * 9 ** (k-2)
            end
        else
            ans += n[0].to_i * 9 ** (k-1)
        end
    else
        ans += 9 ** k
    end
end

puts ans