Recursive Binary Search

Sometimes it’s very convenient to implement the binary search recursively. You’re asked to implement a binary search function that would return the index of the leftmost target element from the array if it was found and -1 otherwise.

Input

The first line of the input contains two integers n (1 ≀ n ≀ ) the number of elements and q (1 ≀ q ≀ ) the number of queries.
The next line contains n space-separated integers ( ≀ ≀ ) in increasing order.
The last line contains q space-separated integers ( ≀ ≀ ) the target values.

Output

The program should print q integers representing the result for the corresponding target value (the indexing starts from 0).

Examples

Input
Output
9 3 20 22 23 23 34 49 52 55 58 49 22 24
5 1 -1
Β 

Constraints

Time limit: 8 seconds

Memory limit: 512 MB

Output limit: 1 MB

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