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()

    val dp = Array(N.length + 1) { Array(K + 1) { LongArray(2) { 0L } } }
    dp[0][0][1] = 1
    dp[1][0][0] = 1

    for (i in N.indices) {
        dp[i + 1][0][0] += dp[i][0][0]

        for (k in 1..K) {
            dp[i + 1][k][0] += dp[i][k][0]

            if (N[i] == '0') {
                dp[i + 1][k][1] += dp[i][k][1]
            } else {
                dp[i + 1][k][1] += dp[i][k - 1][1]
                dp[i + 1][k][0] += dp[i][k - 1][1] * (N[i] - '0' - 1)
                dp[i + 1][k][0] += dp[i][k][1]
            }

            dp[i + 1][k][0] += dp[i][k - 1][0] * 9
        }
    }

    println(dp[N.length][K][0] + dp[N.length][K][1])
}