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: Runtime Error)

# import sys
# input = sys.stdin.readline

from itertools import combinations


def get_n(maxv, ln):
    n = 0

    if ln == 3:
        for i0 in range(1, 10):
            if i0 > maxv//100:
                continue
            for i1 in range(1, 10):
                for i2 in range(1, 10):
                    v = i0 * 100
                    v += i1 * 10
                    v += i2
                    if v <= maxv:
                        n += 1

    if ln == 2:
        for i0 in range(1, 10):
            for i1 in range(1, 10):
                v = i0 * 10
                v += i1
                if v <= maxv:
                    n += 1

    if ln == 1:
        for i0 in range(1, 10):
            v = i0
            if v <= maxv:
                n += 1
    return n


def main():
    N = input()
    K = int(input())

    d_n = len(N)
    c_list = [i for i in range(d_n)]

    combs = list(combinations(c_list, K))

    total = 0

    for comb in combs:

        if comb == (0, 1, 2):
            maxv = int(f'{N[int(comb[0])]}{N[int(comb[1])]}{N[int(comb[2])]}')
            n = get_n(maxv, 3)

        elif comb[0:2] == (0, 1):
            if len(comb) == 3:
                maxv = int(f'{N[int(comb[0])]}{N[int(comb[1])]}{"9"}')
            else:
                maxv = int(f'{N[int(comb[0])]}{N[int(comb[1])]}')
            n = get_n(maxv, len(comb))

        elif comb[0] == 0:
            maxv = int(f'{N[int(comb[0])]}{"9"*(len(comb)-1)}')
            n = get_n(maxv, len(comb))

        else:
            n = 9 ** len(comb)

        total += n

    print(total)


if __name__ == '__main__':
    main()