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: Accepted)

fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {
        val sc = MyScanner()
        val n = sc.next().reversed()
        val k = sc.nextInt()

        val dp1 = Array(n.length + 1) { Array(k + 1) { 0L } }
        val dp2 = Array(n.length + 1) { Array(k + 1) { 0L } }
        dp1[0][0] = 1L
        dp2[0][0] = 1L
        for (i in 1..n.length) {
            for (j in 0..k) {
                dp1[i][j] += dp1[i - 1][j]
            }
            for (j in 1..k) {
                dp1[i][j] += dp1[i - 1][j - 1] * 9
            }
            for (j in 0..k) {
                dp2[i][j] += if (n[i - 1] == '0') dp2[i - 1][j] else dp1[i - 1][j]
            }
            if (n[i - 1] != '0') {
                for (j in 1..k) {
                    dp2[i][j] += dp1[i - 1][j - 1] * (n[i - 1] - '0' - 1) + dp2[i - 1][j - 1]
                }
            }
        }

        println(dp2[n.length][k])
    }
}


class MyScanner() {
    private var index = 0
    private var line = listOf<String>()

    fun next(): String {
        while (line.size <= index) {
            line = readLine()!!.split(' ')
            index = 0
        }
        return line[index++]
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextCharArray() = next().toCharArray()
    fun nextChar() = next()[0]

    fun strList(): List<String> {
        index = line.size
        return readLine()!!.split(' ')
    }

    fun intList() = strList().map { it.toInt() }
    fun longList() = strList().map { it.toLong() }
    fun doubleList() = strList().map { it.toDouble() }
}