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)

N = gets.chomp.to_i
K = gets.chomp.to_i

$ans = 0

1.upto(1000) do |i|
  if i > N
    p $ans
    exit
  end
  if i.to_s.split('').count{|e| e != '0'} == K
    $ans += 1
  end
end

def a(t)
  if K == 1
    $ans += 9
  elsif K == 2
    $ans += (t-1) * (9**2)
  else
    $ans += ((t-1) * (t-2) * (9**3)) / 2
  end
end

4.upto(100) do |i|
  if 10**i <= N
    a(i)
  else
    1.upto(i.to_s.split('').first.to_i) do |u|
      if u.to_i < N.to_s.split('').first.to_i
        a(i-1)
      elsif u.to_i == N.to_s.split('').first.to_i
        0.upto(i.to_s.split('')[1].to_i) do |m|
          if m.to_i < N.to_s.split('')[1].to_i
            a(i-2)
          end
        end
      end
    end
  end
end
p $ans