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)

#  愚直に数え上げる方法

import sys

input = lambda: sys.stdin.readline().rstrip()


def solve():

    N = list(map(int, input()))
    K = int(input())

    if K == 1:
        ans = (len(N) - 1) * 9 + N[0]

    elif K == 2:

        if len(N) < 2:
            print(0)
            exit()

        ans = (9 ** 2) * (len(N) - 1) * (len(N) - 2) // 2
        ans += (N[0] - 1) * (len(N) - 1) * 9

        for i in range(1, len(N)):
            if N[i] != 0:
                ans += N[i] + (len(N) - i - 1) * 9
                break

    elif K == 3:

        if len(N) < 3:
            print(0)
            exit()

        ans = (9 ** 3) * (len(N) - 1) * (len(N) - 2) * (len(N) - 3) // 6
        ans += (N[0] - 1) * (9 ** 2) * (len(N) - 1) * (len(N) - 2) // 2

        for i in range(1, len(N) - 1):
            if N[i] != 0:
                ans += (9 ** 2) * (len(N) - i - 1) * (len(N) - i - 2) // 2
                ans += (N[i] - 1) * (len(N) - i - 1) * 9
                for j in range(i + 1, len(N)):
                    if N[j] != 0:
                        ans += N[j] + (len(N) - j - 1) * 9
                        break
                break

    print(ans)


if __name__ == '__main__':
    solve()