E - Almost Everywhere Zero /

### 問題文

1 以上 N 以下の整数であって、 10 進法で表したときに、0 でない数字がちょうど K 個あるようなものの個数を求めてください。

### 制約

• 1 \leq N < 10^{100}
• 1 \leq K \leq 3

### 入力

N
K


### 入力例 1

100
1


### 出力例 1

19


• 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

### 入力例 2

25
2


### 出力例 2

14


• 11,12,13,14,15,16,17,18,19,21,22,23,24,25

### 入力例 3

314159
2


### 出力例 3

937


### 入力例 4

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3


### 出力例 4

117879300


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


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