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)

import math
n=int(input())
k=int(input())
strn=str(n)

ans1=9*(len(strn)-1)+int(strn[0])
#print(ans1)

def fuc1(x):
    strn=str(x)
    return 9*(len(strn)-1)+int(strn[0])

def fuc2(x):
    if x<10:
        return 0
    strn=str(x)
    ans2=fuc1(int(strn[1:]))
    ans2+=(int(strn[0])-1)*(9*(len(strn)-1))
    #print(ans2,"q")
    for i in range(1,len(strn)-1):
        ans2+=9*(9*(len(strn)-i-1))
    return ans2

def fuc3(x):
    if x<100:
        return 0
    ans3=fuc2(int(strn[1:]))
    ans3+=(int(strn[0])-1)*(81*(len(strn)-1)*(len(strn)-2)//2)
    #print(ans3,"z")
    for i in range(1,len(strn)-2):
        ans3+=9*(81*(len(strn)-i-1)*(len(strn)-i-2)//2)
    #print(ans3)
    return ans3

if k==1:
    print(fuc1(n))
if k==2:
    print(fuc2(n))
if k==3:
    print(fuc3(n))