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: Wrong Answer)

import sys
n = int(input())
k = int(input())

if n < 1000:
    result = 0
    for i in range(n + 1):
        if len(str(i)) - str(i).count("0") == k:
            result += 1
    print(result)
    sys.exit(0)

keta = len(str(n))
firstdigit = int(str(n)[0])


def sigma(n):
    result = 0
    for i in range(1, n + 1):
        result += i
    return result

result = 0
if k == 3:
    # 3桁の任意の数字に0を足していくパターン
    basetype3 = 9 ** 3
elif k == 2:
    # 2桁の任意の数字に0を足していくパターン
    basetype = 9 ** 2
    result += basetype * sigma(keta - 2)
    # 一番高い桁の値が一つ低い値の場合は同様に自由に0を足せる
    result += (firstdigit - 1) * 9 * sigma(keta - 2)
elif k == 1:
    # 1桁の任意の数字に0を足していくパターン
    basetype = 9
    result += basetype * (keta - 1)
    result += firstdigit  # n == 301のような場合には100と200と300
print(result)