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 = input()
k = int(input())
 
dp = [[0] * (k + 2) for _ in range(2)]
dp[0][0] = 1
 
for d in n:
    ndp = [[0] * (k + 2) for _ in range(2)]
    for i in range(k + 1):
        ndp[1][i] += dp[1][i]
        ndp[1][i + 1] += dp[1][i] * 9
        if d == '0':
            ndp[0][i] += dp[0][i]
        else:
            ndp[1][i] += dp[0][i]
            ndp[1][i + 1] += dp[0][i] * (int(d) - 1)
            ndp[0][i + 1] += dp[0][i]
    dp = ndp
print(dp[0][k] + dp[1][k])