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 Python (3.4.3) (judge verdict: Accepted)

def f2(n):
    c = len(n)-1
    nn = n[1:]
    s = c*(c-1)//2 * 9*9 
    s += c * (int(n[0])-1)*9
    nn = str(int(nn))
    s += (len(nn)-1)*9 + int(nn[0])
    return s

n = input()
k = int(input())

if k == 1:
    print((len(n)-1)*9 + int(n[0]))
if k == 2:
    if len(n) >= 2:
        print(f2(n))
    else:
        print(0)
        
if k == 3:
    if len(n) >= 3:
        c = len(n)-1
        nn = n[1:]
        nn = str(int(nn))
        s = c*(c-1)*(c-2)//(3*2) * 9*9*9
        s += (int(n[0])-1) * c*(c-1)//2 * 9*9 
        if len(nn) >= 2:
            s += f2(nn)
        print(s)
    else:
        print(0)