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 Scala (2.11.7) (judge verdict: Runtime Error)

object Main extends App {
	val sc = new java.util.Scanner(System.in)
	val pw = new java.io.PrintWriter(System.out)
	
	val n = sc.next
	val k = sc.nextInt
	val d = n.size - 1
	
	pw.println((if (d < k) 0 else d * Math.pow(Math.pow(9, k), k)).toInt +
			   (1 to k).map(i => (n(i-1).asDigit - 1) * Math.pow(9, k - i)).sum.toInt + 1)
	pw.flush()
}