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)

from math import factorial
def comb(n,k):
    if n>=k:
        return int(factorial(n)/(factorial(k)*factorial(n-k)))
    else:
        return 0

def calc(a,k):
        t = len(a)
        t1 = len(a) - 1
        if k<1 or t == 0:
            return 0
        else:
            if a[t1]>0:
                ans = (9**k)*comb(t1,k) + (9**(k-1))*(a[t1]-1)*comb(t1,k-1)
                ans+=calc(a[:(t-1)],k-1)
            else:
                ans = 0
                ans+=calc(a[:(t-1)],k)
            if a[-k]>=1 and k == 1:
               ans+=1
            return ans

n = int(input())
k = int(input())
number = []
while n:
    number.append(n%10)
    n//=10

t = len(number)
t1 = len(number) - 1

if t>=k:
    ans = 0
    ans += calc(number,k)
else:
    ans = 0
print(ans)