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_string = input()
l = len(N_string)
N = int(N_string)
K = int(input())

n = int(N_string[0])
dp0 = [[n - 1, 0, 0]]
dp1 = [[1, 0, 0]]

for i in range(l - 1):
    n = int(N_string[i + 1])
    if n == 0:
        dp0.append([9 + dp0[i][0],
                    dp0[i][0] * 9 + dp0[i][1],
                    dp0[i][1] * 9 + dp0[i][2]])
        dp1.append([dp1[i][0], dp1[i][1], dp1[i][2]])
    else:
        dp0.append([9 + dp0[i][0] + dp1[i][0],
                    dp0[i][0] * 9 + dp0[i][1] + dp1[i][0] * (n - 1) + dp1[i][1],
                    dp0[i][1] * 9 + dp0[i][2] + dp1[i][1] * (n - 1) + dp1[i][2]])
        dp1.append([0, dp1[i][0], dp1[i][1]])
print(dp0[-1][K - 1] + dp1[-1][K - 1])