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.chomp
K = gets.to_i

case K
when 1
  puts (N.size-1) * 9 + N[0].to_i
when 2
  wk = 0
  wk += (N.size-1) * (N.size-2) / 2 * 81 if N.size > 2
  wk += (N[0].to_i - 1) * 9 * (N.size-1)
  (1...N.size).each{|i|
    next if N[i] == '0'
    wk += 9 * (N.size-1-i) + N[i].to_i
    break
  }
  puts wk
when 3
  wk = 0
  wk += ((N.size-2)**3 - (N.size-2)) / 6 * 729 if N.size > 3
  wk += (N[0].to_i - 1) * 81 * (N.size-1) * (N.size-2) / 2
  cnt = 0
  (1...N.size).each{|i|
    next if N[i] == '0'
    wk += 9 * (N.size-1-i) * (N[i].to_i - 1) if cnt == 0
    wk += 81 * (N.size-1-i) * (N.size-2-i) / 2 if cnt == 0 && i < N.size-1
    wk += 9 * (N.size-1-i) + N[i].to_i if cnt == 1
    cnt += 1
    break if cnt == 2
  }
  puts wk
end