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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	var N string
	var K int
	fmt.Scan(&N, &K)
	d := len(N)
	var dp [2][5][111]int

	dp[0][0][0] = 1
	for i := 0; i < d; i++ {
		for k := 0; k < 4; k++ {
			for x := 0; x < 10; x++ {
				k2 := k
				if x != 0 {
					k2 = k + 1
				}
				dp[1][k2][i+1] += dp[1][k][i]
				if int(N[i]-'0') == x {
					dp[0][k2][i+1] += dp[0][k][i]
				} else if int(N[i]-'0') > x {
					dp[1][k2][i+1] += dp[0][k][i]
				}
			}
		}
	}
	ans := dp[0][K][d] + dp[1][K][d]
	fmt.Println(ans)
}