Given a string $S$. Find the longest string appearing at least $k$ times in $S$.
### Input
- The first line contains a string $S$.
- The second line contains an integer $k$.
### Output
- Print the length of the longest string appearing at least $k$ times in $S$.
### Constraints
- $1 \le k \le |S| \le 10^5$.
### Example
Input:
```
aababbb
2
```
Output:
```
2
```
#### Note: String `ab`.