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)

s = gets.chomp
k = gets.to_i
m = s.length

dp = Array.new(2){Array.new(m+1){[0]*(k+2)}}
dp[1][0][0] = 1

m.times do |i|
  (k+1).times do |j|
    d = s[i].to_i
    if d == 0
      dp[0][i+1][j] += dp[0][i][j]
      dp[1][i+1][j] += dp[1][i][j]
    else
      dp[0][i+1][j] += dp[0][i][j] + dp[1][i][j]
      dp[1][i+1][j+1] += dp[1][i][j]
    end
    dp[0][i+1][j+1] += dp[0][i][j] * 9 + dp[1][i][j] * [0, d-1].max
  end
end

p dp[0][m][k] + dp[1][m][k]