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 (2.4.0) (judge verdict: Accepted)

def I(): return int(input())
def MI(): return map(int, input().split())
def LMI(): return list(map(int, input().split()))


# dp[i + 1][smaller][j] = 上からi桁目までで0でない桁がj個ある数字の数
N = input()
K = I()
l = len(N)
dp = [[[0] * (K + 1) for _ in range(2)] for _ in range(l + 1)]
dp[0][False][0] = 1
for i in range(1, l + 1):
    N_i = int(N[i - 1])
    for smaller in [True, False]:  # smaller := Nより小さいことが確定している
        for j in range(K + 1):
            for d in range((9 if smaller else N_i) + 1):
                if j - (0 if d == 0 else 1) >= 0:
                    dp[i][smaller or d < N_i][j] += dp[i - 1][smaller][j - (0 if d == 0 else 1)]

print(dp[l][True][K] + dp[l][False][K])