A binary search tree (BST) is built from an empty tree by inserting the given keys one at a time, in the order they appear (go left for smaller keys, right for larger, dropping the key at the first empty spot). All inserted keys are distinct.\n\nThen you are given several independent queries. For each query value x, report the floor of x: the largest key stored in the tree that is less than or equal to x. If no stored key is <= x, output the word NONE for that query instead.\n\n## Input format\n\nLine 1: two integers n and q.\nLine 2: n distinct space-separated integers giving the insertion order.\nLine 3: q space-separated integers, the query values.\n\n## Output format\n\nq lines. Line i is the floor of the i-th query, or NONE if no key is <= x.\n\n## Constraints\n\n- 1 <= n <= 100000\n- 1 <= q <= 100000\n- -1000000000 <= each key <= 1000000000, and all keys are distinct.\n- -1000000000 <= each query value <= 1000000000.