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(c) for c in input()]
k = int(input())
dp0 = [1, n[0] - 1] + [0 for j in range(2, k + 1)]
dp1 = [0, 1] + [0 for j in range(2, k + 1)]
for i in range(2, len(n) + 1):
    for j in range(k, 0, -1):
        dp0[j] = (dp0[j - 1] * 9 + dp0[j] + dp1[j - 1] * max(n[i - 1] - 1, 0)
                  + dp1[j] * int(n[i-1] != 0))
    if n[i - 1] != 0:
        dp1 = [0] + dp1[:-1]
print(dp0[-1] + dp1[-1])