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 (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

func Scan() string {
	sc.Scan()
	return sc.Text()
}
func rScan() []rune {
	return []rune(Scan())
}
func iScan() int {
	n, _ := strconv.Atoi(Scan())
	return n
}
func fScan() float64 {
	n, _ := strconv.ParseFloat(Scan(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func SScan(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scan()
	}
	return a
}
func iSScan(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = iScan()
	}
	return a
}
func abs(x int) int {
	if x < 0 {
		x = -x
	}
	return x
}
func mod(x, d int) int {
	x %= d
	if x < 0 {
		x += d
	}
	return x
}
func larger(a, b int) int {
	if a < b {
		return b
	} else {
		return a
	}
}
func smaller(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}
func max(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x < a[i] {
			x = a[i]
		}
	}
	return x
}
func min(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x > a[i] {
			x = a[i]
		}
	}
	return x
}
func sum(a []int) int {
	x := 0
	for _, v := range a {
		x += v
	}
	return x
}
func fSum(a []float64) float64 {
	x := 0.
	for _, v := range a {
		x += v
	}
	return x
}
func bPrint(f bool, x string, y string) {
	if f {
		fmt.Println(x)
	} else {
		fmt.Println(y)
	}
}
func iSSPrint(x []int) {
	fmt.Println(strings.Trim(fmt.Sprint(x), "[]"))
}

var lp int = 1000000007

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, lp)
	sc.Split(bufio.ScanWords)
	n := Scan()
	k := iScan()
	ans := 0
	if k == 3 && len(n) >= k {
		ans += (len(n) - 1) * (len(n) - 2) * (len(n) - 3) / 6 * 9 * 9 * 9
		ans += (stringToInt(string(n[0])) - 1) * (len(n) - 1) * (len(n) - 2) / 2 * 9 * 9
		for i := 1; i < len(n); i++ {
			if string(n[i]) != "0" {
				n = n[i:]
				break
			}
		}
		k--
	}
	if k == 2 && len(n) >= k {
		ans += (len(n) - 1) * (len(n) - 2) / 2 * 9 * 9
		ans += (stringToInt(string(n[0])) - 1) * (len(n) - 1) * 9
		for i := 1; i < len(n); i++ {
			if string(n[i]) != "0" {
				n = n[i:]
				break
			}
		}
	}
	if len(n) != 0 {
		ans += stringToInt(string(n[0])) + (len(n)-1)*9
	}
	fmt.Println(ans)
}