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: Wrong Answer)

require 'set'; require 'prime'
INF=Float::INFINITY; MOD=10**9+7
ar = gets.chomp.split(//).map(&:to_i)
k = gets.chomp.to_i
size = ar.size

def solve1(ar)
  ans = 0
  ar.each_with_index do |e, i|
    if e > 0
      ans += e
      ans += (ar.size - i - 1) * 9
      break
    end
  end
  ans
end

ans = 0
if k == 1
  ans = ar.shift
  ans += (size-1) * 9
  ans = -1
elsif k == 2
  if size <= 1
    puts 0
    exit
  end
  ans += (size-1) * (size-2) / 2 * 9 * 9
  ans += (ar.shift - 1) * (size - 1) * 9
  ans += solve1(ar)
#  ar.each_with_index do |num, i|
#    ans += (num - 1) * (size - i - 1) * 9
#  end

else
  if size <= 2
    puts 0
    exit
  end

  ans += (size-1) * (size-2) * (size-3) / 6 * 9 * 9 * 9
  ans += (ar.shift - 1) * (size-1) * (size-2) / 2 * 9 * 9
  size2 = ar.size
  ans += (size2-1) * (size2-2) / 2 * 9 * 9
  ans += (ar.shift - 1) * (size2 - 1) * 9
  ans += solve1(ar)
end

puts ans