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)

#ひどいアルゴリズムができてしまった

def conv(a,b)
  if b > a/2
    b = a - b
  end
  ans = 1
  div = 1
  b.times do |i|
    ans *= a - i
    div *= (i+1)
  end
  ans = ans / div
end

def calc(n,k)
  if n.to_s.length < k
    0
  elsif  ( n.to_s =~ /[^9]/ ) == nil
    9**k*conv(n.to_s.length,k)
  elsif k == 0
    1
  elsif n < 10
    n
  else
    #最初の桁が0の場合　+ 最初の桁が0以外の場合
    calc(10 ** (n.to_s.length-1) -1,k) + (n.to_s[0].to_i - 1) * calc(10 ** (n.to_s.length-1) -1,k-1) + calc(n.to_s[1..-1].to_i,k-1)
  end
end

n = gets.to_i
k = gets.to_i
puts calc(n,k)