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)

n = "0" + gets.chomp
kkk = gets.chomp.to_i
# 桁, 回数,  0→それまでの桁と確定してる桁が同じ 1→小さいので何でも入る
dp = Array.new(n.length + 1).map{Array.new(kkk + 1)}.map{|a| a.map{Array.new(2,0)}}
dp[0][0][0] = 1

n.length.times do |i|
	now = n[i].to_i
	(kkk+1).times do |j|
		2.times do |k|
			10.times do |d|
				ii = i + 1; jj = j; kk = k;
				jj += 1 if d != 0
				next if jj > kkk
				if k == 0 then
					next if d > now
					kk = 1 if d < now
				end
				#puts "i:#{i} j:#{j} k:#{k} ii:#{ii} jj:#{jj} kk:#{kk}"
				dp[ii][jj][kk] += dp[i][j][k]
			end
		end
	end
end 
puts dp[n.length][kkk].inject(:+)


# (1..n.length-1).times do |i|
# 	now = n[i].to_i