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.to_i
K = gets.to_i
keta = N.to_s.length
first = N.to_s[0].to_i
result = 0

nums_list = (1..9).to_a.repeated_permutation(K-1).to_a
(0..(keta-1)).to_a.combination(K) do |arr|
  if arr[-1] < keta-1
    result += 9**K
    next
  end
  result += (first - 1) * (9**(K-1))
  base = first * (10**arr[-1])
  nums_list.each do |nums|
    x = base
    nums.each_with_index do |nn, index|
      x += nn * (10**arr[index])
    end
    if x <= N 
      result += 1
    end
  end
end
puts result