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)

n=input()
k=int(input())
m=len(n)

dp=[[[0]*2 for _ in range(4)] for _ in range(m+1)]

dp[0][0][0]=1
for i in range(m):
  keta=int(n[i])
  for j in range(3):
    dp[i+1][j][0]+=dp[i][j][0]*(keta==0)
    dp[i+1][j+1][0]+=dp[i][j][0]*(keta!=0)
    dp[i+1][j][1]+=dp[i][j][0]*(keta>0)+dp[i][j][1]
    dp[i+1][j+1][1]+=dp[i][j][0]*max(keta-1,0)+dp[i][j][1]*9
                      
print(dp[m][k][0]+dp[m][k][1])