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)

def comb(n,r)
  return 0 if r > n || n < 0
  r.times.inject(1){|s,i| s * (n - i) / (i + 1) }
end
N = gets.chomp.chars.map(&:to_i)
K = gets.to_i
ans = (N.size - N.count(0) == K ? 1 : 0)

N.each.with_index(1).inject(0) do |nz,(d, i)|
  if nz == K
    ans += 1
    break
  end
  
  t = N.size - i
  if !d.zero?
    ans += (d - 1) * comb(t, K - nz - 1) * (9 ** (K - nz - 1))
    ans += comb(t, K - nz) * (9 ** (K - nz))
    nz + 1
  else
    nz
  end
end
puts ans