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)

from scipy.misc import comb
def solve(i,k,smaller):
    if i == len(S):
        if k == 0:
            #0以外の個数がkと等しいので答えとしてカウントできる
            return 1
        else:
            #0以外の個数がkと等しくないので答えとしてカウント不可
            return 0 
    
    if k ==0:
        #kの個数を使い切りこれ以上下の桁は0で埋まり1通りの為
        return 1
    
    if smaller :
        return comb(len(S)-i,k)*pow(9,k)
    else:
        if S[i] =="0":
            return solve(i+1,k,False)
        else:
            zero = solve(i+1,k,True)
            aida = solve(i+1,k-1,True)*(int(S[i])-1)
            ici  = solve(i+1,k-1,False)
            return zero+aida+ici
            
N = int(input())
S = str(N)
K = int(input())

ans = solve(0,K,False)
print(ans)