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: Accepted)

N=chomp(readline())
K=parse(Int,readline())
dp=zeros(Int,length(N)+1,2,4)
dp[1,1,1]=1
for i=1:length(N),j=1:2
	lim=j==1 ? Int(N[i])-48 : 9
	for k=1:K+1,l=0:lim
		nk=k+(l!=0)
		nj=j==2||l<lim ? 2 : 1
		if nk<=K+1
			dp[i+1,nj,nk]+=dp[i,j,k]
		end
	end
end
println(dp[length(N)+1,1,K+1]+dp[length(N)+1,2,K+1])