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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$num = trim(fgets(STDIN));
$k = intval(fgets(STDIN));

$dp0 = array_fill(0, strlen($num)+1, array_fill(0, $k+1, 0));//not-max
$dp1 = array_fill(0, strlen($num)+1, array_fill(0, $k+1, 0));//max
$dp1[0][0] = 1;// N桁目 - 0以外の数
for($i = 1; $i <= strlen($num); $i++){
    for($j = 0; $j <= $k; $j++){
        $d = $num[$i-1];
        if($d == 0){
            $dp1[$i][$j] += $dp1[$i-1][$j];
        }else{
            $dp1[$i][$j] += $dp1[$i-1][$j-1] ?? 0;
        }
        $dp0[$i][$j] += ($dp0[$i-1][$j - 1]??0) * 9 + $dp0[$i-1][$j] + ($d ? $dp1[$i-1][$j] + ($dp1[$i-1][$j-1]??0) * ($d-1): 0);
    }
}
echo $dp0[strlen($num)][$k] + $dp1[strlen($num)][$k];