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.chars
K = gets.chomp.to_i

n = S.length

# DP [i][j][k]
# i桁目まで見たときに、j個の非0があって、k 0-> Nと一致 1-> N以下

dp = Array.new(n+1).map{Array.new(K+1).map{Array.new(2,0)}}

# 0桁目まで見たときはNと一致してるので最後は0
dp[0][0][0] = 1

n.times do |i|
  num = S[i].to_i

  (K+1).times do |j|
    2.times do |k|
      10.times do |d|
        # iは次の桁
        ni = i + 1
        nj = j
        nk = k

        # 非ゼロなら+1
        nj += 1 unless d == 0

        # K個を超えてしまったらnext
        next if nj > K

        # 一致してるとき
        if k == 0
          next if d > num
          nk = 1 if d < num
        end

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

p dp[n][K][0] + dp[n][K][1]