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 (3.8.2) (judge verdict: Accepted)

# -*- coding: utf-8 -*-
import sys 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
MOD = 10**9+7   
N = readline().decode().rstrip()
K = int(readline())
L = len(N)
# 桁DP
dp = [[[0 for _ in range(2)] for _ in range(4)] for _ in range(L+1)]
dp[0][0][0] = 1
for i in range(L):
    for j in range(4):
        for k in range(2):
            nd = int(N[i])
            for d in range(10):
                ni = i + 1; nj = j; nk = k
                if d != 0:
                    nj += 1
                if nj > K:
                    continue
                if k == 0:
                    if d > nd:
                        continue
                    if d < nd:
                        nk = 1
                dp[ni][nj][nk] += dp[i][j][k]
print(dp[L][K][0]+dp[L][K][1])