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).