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)

fc=->x,y{
  (1..y).reduce(1){|s,i|
    s*(x-y+i)/i
  }
}
f0=->d,x{
  fc[d,x]*9**x
}
f=->n,k{
  return 1 if k==0
  nstr=n.to_s
  d=nstr.size
  return 0 if d<k
  return n if d==1
  f0[d-1,k]+(nstr[0].to_i-1)*f0[d-1,k-1]+f[nstr[1..-1].to_i,k-1]
}
puts f[*$<.map(&:to_i)]