Given an array A of n integers and q queries, each is an integers k.
For each query, find the longest subarray contains only elements not bigger than k.
### Input
- The first line contains 2 integers n,q.
- The second line contains n integers Ai.
- The next q lines, each line contains an integer k, a query.
### Output
- Print q lines, the ith is the answer to query i.
### Constraints
- 1≤n≤105.
- 0≤|Ai|,|k|≤109.
### Example
Input:
64-25610-50-105-411
Output:
0216