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 = gets.chomp.to_i
K = gets.chomp.to_i
answer = 0
a = Array.new(0)
if K == 1
    while n > 10
        n /= 10
        answer += 9
    end
    answer += n
elsif K == 2
    if n <= 10
        answer = 0
    elsif n <= 100
        answer += (n/10-1)*9
        answer += n%10
    else
        while n >= 10
            a.push(n%10)
            n /= 10
        end
        a.push(n)
        s = a.size
        answer += (s-1)*(s-2)/2*81 + (s-1)*(a[-1]-1)*9
        l = 1
        m = 2
        while l < 2 && m <= s
            if a[-m] != 0
                answer += a[-m] + (s-m)*9
                l += 1
            end
            m += 1
        end 
    end 
else
    if n <= 100
        answer = 0
    else
        while n >= 10
            a.push(n%10)
            n /= 10
        end
        a.push(n)
        s = a.size
        answer += (s-1)*(s-2)*(s-3)/6*729 + (s-1)*(s-2)/2*(a[-1]-1)*81
        l = 1
        m = 2
        while l < 3 && m <= s
            if a[-m] != 0
                if l == 1
                    answer += (s-m)*(s-m-1)/2*81 + (a[-m]-1)*(s-m)*9
                else
                    answer += a[-m] + (s-m)*9
                end
                l += 1
            end 
            m += 1
        end
    end
end
puts answer