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.to_i
k=gets.to_i
s=n.to_s
a=s.chars.map(&:to_i)
z=s.size
def f1(n,s,a,z)
  if n==0
    return 0
  else
    return (z-1)*9+a[0]
  end
end
def f2(n,s,a,z)
  if z==1
    return 0
  else
    c=(z-2)*(z-1)/2*81+(z-1)*9*(a[0]-1)
    a.delete_at(0)
    z=a.size
    s=a.join
    n=s.to_i
    c+=f1(n,s,a,z)
    return c
  end
end
def f3(n,s,a,z)
  if z<=2
    return 0
  else
    c=(z-3)*(z-2)*(z-1)/6*729+(z-2)*(z-1)/2*81*(a[0]-1)
    a.delete_at(0)
    z=a.size
    s=a.join
    n=s.to_i
    c+=f1(n,s,a,z)
    return c
  end
end
if k==1
  puts (z-1)*9+a[0]
elsif k==2
  puts f2(n,s,a,z)
else
  puts f3(n,s,a,z)
end