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: Runtime Error)

def factorial(a):
    r = 1
    for i in range(a):
        r *= i+1
    return r

def combinations(a, b):
    if a>=0 and b>=0 and a >= b:
        return pow(9, b) * factorial(a) // factorial(b) // factorial(a-b)
    else:
        return 0

def count(m, a, b):
    # return the count of numbers in range [0, m x 10^a] with b non zero digitals
    ## the count of numbers in range [0, m x 10^a) with b non zero digitals
    r = combinations(a-1, b) + (m-1) * combinations(a-1, b-1)
    if b == 1:
        ## m x 10^a
        r += 1
    return r

N = int(input())
K = int(input())

digit = list(map(int, str(N)))
M = len(digit)

C = 0
for i in range(K):
    C += count(digit[i], M-i, K-i)

print(C)