D. Power Up
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given $$$n$$$ elements with distinct power levels $$$p_1,p_2,\dots,p_n$$$.

In one operation, you choose two different elements with power levels $$$a$$$ and $$$b$$$ and combine them into a hybrid. The hybrid's power level is

$$$$$$a \cdot b + 2(a+b).$$$$$$

For example, if you choose elements with power levels $$$6$$$ and $$$7$$$, the hybrid has power level $$$6 \cdot 7 + 2 \cdot (6+7) = 68$$$.

You are given $$$q$$$ independent queries. For each query value $$$x$$$, determine whether there exists a pair of different elements from the list such that combining them in one operation produces a hybrid with power level exactly $$$x$$$.

Input

The first line contains two integers $$$n$$$ and $$$q$$$ $$$(1 \le n \le 2 \cdot 10^5,\ 1 \le q \le 2 \cdot 10^5)$$$.

The second line contains $$$n$$$ distinct integers $$$p_1,p_2,\dots,p_n$$$ $$$(1 \le p_i \le 2 \cdot 10^5)$$$.

Each of the next $$$q$$$ lines contains one integer $$$x$$$ $$$(1 \le x \le 10^9)$$$ — the value of a query.

Output

For each query, output YES (case-insensitive) if the query value can be obtained by combining some pair of different elements in one operation, and NO (case-insensitive) otherwise.

Examples
Input
5 8
1 3 4 6 7
11
21
26
36
50
68
69
20
Output
YES
NO
YES
YES
YES
YES
NO
YES
Input
4 6
2 4 1 3
8
25
14
11
16
8
Output
YES
NO
YES
YES
YES
YES