The only difference between easy and hard versions is the maximum values of $$$n$$$ and $$$q$$$.

You are given an array, consisting of $$$n$$$ integers. Initially, all elements are red.

You can apply the following operation to the array multiple times. During the $$$i$$$-th operation, you select an element of the array; then:

if the element is red, it increases by $$$i$$$ and becomes blue;
if the element is blue, it decreases by $$$i$$$ and becomes red.

The operations are numbered from $$$1$$$, i. e. during the first operation some element is changed by $$$1$$$ and so on.

You are asked $$$q$$$ queries of the following form:

given an integer $$$k$$$, what can the largest minimum in the array be if you apply exactly $$$k$$$ operations to it?

Note that the operations don't affect the array between queries, all queries are asked on the initial array $$$a$$$.

Input

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n, q \le 2 \cdot 10^5$$$) — the number of elements in the array and the number of queries.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The third line contains $$$q$$$ integers $$$k_1, k_2, \dots, k_q$$$ ($$$1 \le k_j \le 10^9$$$).

Output

For each query, print a single integer — the largest minimum that the array can have after you apply exactly $$$k$$$ operations to it.

Red-Blue Operations (Hard Version)

Examples