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: Wrong Answer)

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

def C(n,r):
  if n>=r:
    return factorial(n)//factorial(r)//factorial(n-r)
  else:
    return 0

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

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