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: Accepted)

N = gets.to_i
K = gets.to_i
L = N.to_s.length

dp = Array.new(105){Array.new(4){Array.new(2, 0)}}
dp[0][0][0] = 1
L.times do |p|
  nd = N.to_s[p].to_i
  4.times do |q|
    2.times do |r|
      10.times do |d|
        np, nq, nr = p + 1, q, r
        if d != 0
          nq += 1
        end
        
        if nq > K
          next
        end
        
        if nr == 0
          if d > nd
            next
          elsif d < nd
            nr = 1
          end
        end
        dp[np][nq][nr] += dp[p][q][r]
      end
    end
  end
end

puts dp[L][K][0] + dp[L][K][1]