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 = int(input())
K = int(input())
A = 0
if N <= 100000:
    for i in range(1,N+1):
        c = str(i)
        d = len(c) - c.count('0')
#    print(i,c,d,len(c),c.count('0'))
        if d == K:
            A += 1
else:
    keta = len(str(N))
    if K ==1:
        A = 9*(keta-1)
    if K ==2:
        A = 9*9*(keta-1)*(keta-2)//2
        print(A)
    if K ==3:
        A = 9*9*9*(keta-1)*(keta-2)*(keta-3)//6
    nc = 1
    print(N,K,keta,A)
    while nc <= 3 and keta >=1:
        # abcd... -> 1000000 - a0000000
        T = N//(10**(keta-1))%10
        print(T,nc)
        if T == 0:
            keta -=1
        else:
            if (nc == 1 and K==1) or (nc==2 and K==2) or (nc==3 and K==3):
              A = A + (T)
            if ((nc == 1 and K ==2) or (nc ==2 and K==3)):
                A = A + int((T-1)*9*(keta-1))
            if (nc==2 and K==2):
                A = A + 9*(keta-1)
            if (nc==1 and K ==3):
                A = A + int((T-1)*9*9*(keta-1)*(keta-2)/2)
            if (nc==2 and K==3):
                A = A + 9*9*(keta-1)*(keta-2)/2
            nc +=1
            keta -=1
        print(A)
        
print(A)