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 numpy as np

N=int(input())
n=[int(i) for i in str(N)]
K=int(input())
L=len(n)
dp=np.zeros((L+1,2,K+1),dtype=int)
dp[0,0,0]=1

for i in range(L):
  for smaller in [0,1]:
    for j in range(0,K):
      m=10 if smaller else n[i]+1
      for x in range(m):
        #i桁目がxだったときにdp[i][smaller][j]をどこに足しますか？
        dp[i+1][smaller or x<n[i]][j+(x!=0)]+=dp[i][smaller][j]
        
print(dp[L,:,K].sum())