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)

N = [int(i) for i in input()]
n = len(N)
K = int(input())
lis = [0]*3
foo = 0
for i in range(n):
    if N[i]!=0:
        lis[foo] = i
        foo += 1
    if foo==3:
        break



if n < K:
    print(0)
else:
    if K ==3:
        ans = (n-1)*(n-2)*(n-3)*9**3//6
        ans += (N[0]-1)*(n-1)*(n-2)*9**2 //2
        if lis[1]!=0:
            ans += (n-1-lis[1])*(n-2-lis[1])*9**2//2
        if lis[2]!=0:
            ans += (N[lis[1]]-1)*(n-1-lis[1])*9 +(n-1-lis[2])*9 +N[lis[2]]
    elif K ==2:
        ans = (n-1)*(n-2)//2 *9**2 +(N[0]-1)*(n-1)*9
        if lis[1]!=0:
            ans += (n-1-lis[1])*9 +N[lis[1]]
    elif K ==1:
        ans = 9*(n-1) +N[0]

    print(max(0,ans))