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≤k≤|S|≤105.
### Example
Input:
aaba2
Output:
2
#### Note: String ab.