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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

#coding:utf-8
import sys,os
from collections import defaultdict, deque
from fractions import gcd
from math import ceil, floor
sys.setrecursionlimit(10**6)
write = sys.stdout.write
dbg = (lambda *something: print(*something)) if 'TERM_PROGRAM' in os.environ else lambda *x: 0
def main(given=sys.stdin.readline):
    input = lambda: given().rstrip()
    LMIIS = lambda: list(map(int,input().split()))
    II = lambda: int(input())
    XLMIIS = lambda x: [LMIIS() for _ in range(x)]
    YN = lambda c : print('Yes') if c else print('No')
    MOD = 10**9+7

    list_N = list(map(int,list(input())))
    len_N = len(list_N)
    list_N = [0] + list_N
    dbg(list_N)
    K = II()
    dp0 = []
    dp1 = []
    for i in range(len_N+1):
        dp0.append([0]*(K+1))
        dp1.append([0]*(K+1))
    for i in range(1,len_N+1):
        dp0[i][0] = 1
    dp0[1][1] = max(list_N[1]-1,0)
    dp1[1][1] = 1
    for i in range(2,len_N+1):
        for j in range(1,K+1):
            dp0[i][j] = dp0[i-1][j-1] * 9 + dp0[i-1][j]
            dp1[i][j] = dp1[i-1][j-1] * list_N[i] + dp1[i-1][j]
    print(dp0[len_N][K]+dp1[len_N][K])
    dbg(dp0[len_N][K],dp1[len_N][K])






if __name__ == '__main__':
    main()