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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	a = parseMap(split(chomp(readline()),""))
	k = readline() |> parseInt
	n = length(a)
	dp = zeros(Int,n,k+1,2)
	dp[1,2,1] = a[1]-1
	dp[1,2,2] = 1
	dp[1,1,1] = 1
	for i in 2:n
		for j in 1:k+1
			dp[i,j,1] += dp[i-1,j,1]+dp[i-1,j,2]
			if a[i] == 0
				dp[i,j,2] = dp[i-1,j,2]
			else
				dp[i,j,2] = 0
			end
			if j>1
				dp[i,j,1] += dp[i-1,j-1,1]*9+dp[i-1,j-1,2]*(max(a[i]-1,0))
				if a[i]>0
					dp[i,j,2] = dp[i-1,j-1,2]
				else
					dp[i,j,2] = 0
				end
			end
		end
	end
	println(dp[n,k+1,1]+dp[n,k+1,2])
end

main()