C. Bessie and Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Bessie is given an array $$$a$$$ of length $$$n$$$ and wants to know whether it's possible to reverse the array by swapping pairs of elements exactly $$$k$$$ times. Can you help her?

Answer $$$q$$$ queries.

Input

The first line contains two space-separated integers $$$n$$$ and $$$q$$$ ($$$2 \le n, q \le 2\cdot10^{5}$$$), the array $$$a$$$'s length and the number of queries, respectively.

The next line contains $$$n$$$ space-separated integers $$$a_1, a_2, ..., a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$).

The next $$$q$$$ lines each contain a positive integer $$$k$$$ ($$$1 \le k \le 10^9$$$).

Output

Output, for each query, YES if exactly $$$k$$$ swaps are sufficient to transform the array into its desired form, and NO otherwise. This is not case-sensitive; for example, Yes, yEs, and yes are all allowed.

Examples
Input
4 3
4 1 2 3
2
3
4
Output
YES
NO
YES
Input
6 2
3 2 2 1 3 4
2
3
Output
NO
YES
Note

The following information pertains to the first sample input.

For the first query ($$$k = 2$$$), the array can be reversed in $$$2$$$ operations:

OperationArray
Initial$$$[4, 1, 2, 3]$$$
Swap $$$a_1$$$ and $$$a_4$$$$$$[3, 1, 2, 4]$$$
Swap $$$a_2$$$ and $$$a_3$$$$$$[3, 2, 1, 4]$$$

For the second query ($$$k = 3$$$), it can be shown that the array cannot be reversed in exactly $$$3$$$ operations.

For the third query ($$$k = 4$$$), the array can be reversed in $$$4$$$ operations:

OperationArray
Initial$$$[4, 1, 2, 3]$$$
Swap $$$a_1$$$ and $$$a_2$$$$$$[1, 4, 2, 3]$$$
Swap $$$a_2$$$ and $$$a_3$$$$$$[1, 2, 4, 3]$$$
Swap $$$a_3$$$ and $$$a_4$$$$$$[1, 2, 3, 4]$$$
Swap $$$a_1$$$ and $$$a_3$$$$$$[3, 2, 1, 4]$$$