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>) {

    fun pow(n: Int, e: Int): Int {
        return (0 until e).fold(1) { acc, i -> acc * n }
    }

    fun comb(n: Int, k: Int): Int {
        if (k !in (0..n)) return 0
        var r = n
        repeat(k - 1) { r *= n - it - 1 }
        repeat(k - 1) { r /= k - it }
        return r
    }

    val s = readLine()!!
    val k = readLine()!!.toInt()
    val n = s.length

    fun f(i: Int, k: Int, small: Boolean): Int {
        if (i == n) {
            if (k == 0) return 1
            return 0
        }

        if (k == 0) return 1

        if (small) return comb(n - i, k) * pow(9, k)
        
        if (s[i] == '0') return f(i + 1, k, false)

        return f(i + 1, k, true) +
                f(i + 1, k - 1, true) * (s[i] - '1') +
                f(i + 1, k - 1, false)
    }

    println(f(0, k, false))
}