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: Runtime Error)

def nC2(n):
    return n*(n-1)/2

def nC3(n):
    return n*(n-1)*(n-2)/2/3

def K1(s):
    while s[0]=="0" and len(s)>0:
        s=s[1:]

    ll=len(s)
    if ll ==0:
        N=0
    elif ll==1:
        N=int(s[0])
    
    elif ll>1:
        N=int(s[0])+9*(ll-1)


    return N


def K2(s):
    while s[0]=="0" and len(s)>0:
        s=s[1:]
    
    ll=len(s)

    if ll==1 or ll ==0:
        N=0
    elif ll==2:
        N=(int(s[0])-1)*9+int(s[1])
    else:
        N=K1(s[1:])+(int(s[0])-1)*(ll-1)*9+9*9*nC2(ll-1)

    return N


def K3(s):
    ll=len(s)

    if ll ==1 or ll==2 or ll==0:
        N=0
    elif ll==3:
        N=(int(s[0])-1)*9*9+int(s[1])*int(s[2])
    else:
        N=K2(s[1:])+(int(s[0])-1)*nC2(ll-1)*9*9+nC3(ll-1)*9*9*9
    
    return N

N=input()
K=input()

if K=="1":
    ans=K1(N)
elif K=="2":
    ans=K2(N)
elif K=="3":
    ans=K3(N)


print(int(ans))