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)

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

m = len(N)
ans = 1
for i in range(K):
    ans = ans*(m-i)*9//(K-i)
count = K
i = 0

while count and i < m:
    Num = 9-int(N[i])
    for j in range(count-1):
        Num = (Num*(m-1-i-j)*9)//(count-1-j)
    ans -= Num
    # print(Num,i,j,count)
    if int(N[i]) != 0:
        count -= 1
    i += 1

print(ans)