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

@memo = {}

def solve(n, k)
    return @memo[[n, k]] if @memo[[n, k]]
    return 1 if k == 0
    return 0 if n < 1
    return 0 if n.to_s.size < k

    head = n.to_s.chars[0].to_i
    c = n.to_s.chars
    c.shift
    right = c.join.to_i
    v = 10**c.size - 1

    v1 = solve(right, k - 1)
    v2 = (head - 1) * solve(v, k - 1)
    v3 = solve(v, k)

    @memo[[n, k]] = v1 + v2 + v3
end

puts solve(n, k)