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)

from math import factorial
N=int(input())
K=int(input())
#N,K = int(314159),int(3)
S = list(map(int,str(N)))

def C(n,r): 
    return factorial(n) // (factorial(n - r) * factorial(r))

def D(i,j): 
    return (9**j)*C(i,j)

ans = 0
l = len(S)
for i in range(l):
    if K >= 1:
        ans = ans + (int(S[i])-1)*D(l-1,K-1) + D(l-1,K)
        K -= 1
        l -= 1
    else:
        ans += 1
        break
print(ans)