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)

import java.util.*

fun main(args: Array<String>) {
    val N = readString()
    val K = readInt()
    val dp = Array(N.length + 1) { Array(2) { LongArray(K + 1) { 0 } } }
    dp[0][1][0] = 1L

    for (i in 1..N.length) {
        dp[i][0][0] = 1
        dp[i][1][0] = 0
        val n = N[i - 1] - '0'
        for (k in 1..K) {
            dp[i][0][k] = dp[i - 1][0][k] + dp[i - 1][0][k - 1] * 9
            if (n != 0)
                dp[i][0][k] += dp[i - 1][1][k] + dp[i - 1][1][k - 1] * (n - 1)

            dp[i][1][k] = if (n == 0) dp[i - 1][1][k] else dp[i - 1][1][k - 1]
        }
    }
    println(dp[N.length][0][K] + dp[N.length][1][K])
}

fun readString() = readLine()!!
fun readStringList() = readLine()!!.split(" ")
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)