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 Ruby (2.3.3) (judge verdict: Accepted)

s = gets.chomp
K = gets.to_i
N = s.to_s.size

dp = Array.new(105) {Array.new(4) {Array.new(2, 0)}} #動的計画法

dp[0][0][0] = 1

(0...N).each do |i|                            #それぞれの桁の数について 
    (0..K).each do |j|
        (0..1).each do |k|
            nd = s[i].to_i
            (0..9).each do |d|
                ni = i + 1
                nj = d == 0 ? j : j + 1        # 0以外の数字が出てきた回数
                nk = k == 0 && nd == d ? 0 : 1
                
                next if nj > K
                next if k == 0 && nd < d
                next if dp[i][j][k] == 0

                dp[ni][nj][nk] += dp[i][j][k]
            end
        end
    end
end

puts dp[N][K][0] + dp[N][K][1]