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()
L = len(N)
K = int(input())

dp = [[[0]*2 for _ in range(K+1)] for _ in range(L+1)]
dp[0][0][0] = 1
for i,c in enumerate(N):
    c = int(c)
    for k in range(K+1):
        for less in range(2):
            for d in range(10):
                nk = k + (d>0)
                if nk > K: continue
                if less == 0 and d > c: continue
                nxless = not(less==0 and d==c)
                dp[i+1][nk][nxless] += dp[i][k][less]
print(sum(dp[-1][-1]))