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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun C(a: Int, b: Int): Int {
  var r = 1
  for (i in (a - b + 1)..(a)) {
  	r *= i
  }
  
  for (i in 1..b) {
  	r /= i
  }
  
  return r
}

fun pow(a: Int, b: Int): Int {
	return Math.pow(a.toDouble(), b.toDouble()).toInt()
}

fun f(N_Str: String, K: Int): Int {
  if (K == 0) {
  	return 1
  }
  
  val M = N_Str.length
  var res = 0
  for (i in K..M - 1) {
  	res += C(i - 1, K - 1)
  }
  res *= pow(9, K)
  
  val a = N_Str.substring(0, 1).toInt()
  res += (a - 1) * pow(9, K - 1) * C(M - 1, K - 1) 
  
  for (i in 1..M - 1) {
  	if (N_Str[i] == '0') {
    	continue
    } 
   	return res + f(N_Str.substring(i), K - 1)
  }
  
  return res + 1
}

fun main(args: Array<String>) {
  val N_Str = readLine()!!
  val K = readLine()!!.toInt()
  
  println(f(N_Str, K))
}