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>) {
    val n = readLine()!!
    val k = readLine()!!.toInt()

    // 1: Nと一致, 0: Nより真に小さい
    val dp = Array(101) { Array(4) { Array(2) { 0 } } }
    dp[0][0][1] = 1

    var ans = 0
    for (len in n.indices) {
        for (countNotZero in 0..k) {
            for (matchN in 0..1) {
                if (dp[len][countNotZero][matchN] == 0) continue

                for (nextDigit in '0'..'9') {
                    var nextMatchN = matchN
                    if (matchN == 1) {
                        if (nextDigit > n[len]) {
                            continue
                        } else if (nextDigit < n[len]) {
                            nextMatchN = 0
                        }
                    }

                    var nextCountNotZero = countNotZero
                    if (nextDigit != '0') {
                        nextCountNotZero++
                    }

                    if (nextCountNotZero <= k) {
                        dp[len + 1][nextCountNotZero][nextMatchN] += dp[len][countNotZero][matchN]
                    }
                }
            }
        }
    }
    println(dp[n.length][k][0] + dp[n.length][k][1])
}