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 (1.3.71) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStreamReader
import java.io.PrintWriter
import kotlin.math.abs
import kotlin.math.max
import kotlin.math.min

val br = BufferedReader(InputStreamReader(System.`in`))
val out = PrintWriter(System.out)

fun main() {
    br.use { out.use {
        solve()
        out.flush()
    } }
}

fun solve() {
    val s = br.readLine()!!
    val k = readInteger()

    // dp[i][smaller][k] 上位桁からi桁目に0がK個あるときの場合の数
    val dp = Array(s.length + 1) { Array(2) { LongArray(k + 2) } }
    dp[0][0][0] = 1
// 桁dpのお気持ち
//    for (i in s.indices) {
//        val n = s[i] - '0'
//        for (d in 0..9) {
//            dp[i + 1][1] = dp[i][1]
//        }
//
//        for (d in 0 until n) {
//            dp[i + 1][1] = dp[i][0]
//        }
//
//        dp[i + 1][0] = dp[i][0]
//    }

    for (i in s.indices) {
        val n = s[i] - '0'
        for (j in 0..k) {
            for (d in 0..9) {
                if (d == 0) {
                    dp[i + 1][1][j] += dp[i][1][j]
                } else {
                    dp[i + 1][1][j + 1] += dp[i][1][j]
                }
            }

            for (d in 0 until n) {
                if (d == 0) {
                    dp[i + 1][1][j] += dp[i][0][j]
                } else {
                    dp[i + 1][1][j + 1] += dp[i][0][j]
                }
            }

            if (n == 0) {
                dp[i + 1][0][j] += dp[i][0][j]
            } else {
                dp[i + 1][0][j + 1] += dp[i][0][j]
            }
        }
    }
    out.println(dp[s.length][1][k] + dp[s.length][0][k])
}

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)