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 (2.7.1) (judge verdict: Accepted)

n = gets.chomp
m = gets.to_i
size = n.size
dp = Array.new(size + 1) { Array.new(2) { Array.new(size + 1) { 0 } } }
dp[0][0][0] = 1

0.upto(size - 1) do |i|
  2.times do |j|
    size.times do |k|
      d = n[i].to_i
      0.upto(j == 0 ? d : 9) do |l|
        dp[i + 1][j == 1 || l < d ? 1 : 0][l != 0 ? k + 1 : k] += dp[i][j][k]
      end
    end
  end
end

puts size < m ? 0 : dp[size][0][m] + dp[size][1][m]