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E. Sliding Doors
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Imagine that you are the CEO of a big old-fashioned company. Unlike any modern and progressive company (such as JetBrains), your company has a dress code. That's why you have already allocated a spacious room for your employees where they can change their clothes. Moreover, you've already purchased an $$$m$$$-compartment wardrobe, so the $$$i$$$-th employee can keep his/her belongings in the $$$i$$$-th cell (of course, all compartments have equal widths).

The issue has occurred: the wardrobe has sliding doors! More specifically, the wardrobe has $$$n$$$ doors (numbered from left to right) and the $$$j$$$-th door has width equal to $$$a_j$$$ wardrobe's cells. The wardrobe has single rails so that no two doors can slide past each other.

Extremely schematic example of a wardrobe: $$$m=9$$$, $$$n=2$$$, $$$a_1=2$$$, $$$a_2=3$$$.

The problem is as follows: sometimes to open some cells you must close some other cells (since all doors are placed on the single track). For example, if you have a $$$4$$$-compartment wardrobe (i.e. $$$m=4$$$) with $$$n=2$$$ one-cell doors (i.e. $$$a_1=a_2=1$$$) and you need to open the $$$1$$$-st and the $$$3$$$-rd cells, you have to close the $$$2$$$-nd and the $$$4$$$-th cells.

As CEO, you have a complete schedule for the next $$$q$$$ days. Now you are wondering: is it possible that all employees who will come on the $$$k$$$-th day can access their cells simultaneously?

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le 4 \cdot 10^5$$$) — the number of doors and compartments respectively.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le m$$$, $$$\sum{a_i} \le m$$$) — the corresponding widths of the doors.

The third line contains a single integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of days you have to process.

The next $$$q$$$ lines describe schedule of each day. Each schedule is represented as an integer $$$c_k$$$ followed by $$$c_k$$$ integers $$$w_1, w_2, \dots, w_{c_k}$$$ ($$$1 \le c_k \le 2 \cdot 10^5$$$, $$$1 \le w_1 < w_2 < \dots < w_{c_k} \le m$$$) — the number of employees who will come on the $$$k$$$-th day, and their indices in ascending order.

It's guaranteed that $$$\sum{c_k}$$$ doesn't exceed $$$2 \cdot 10^5$$$.

Output

Print $$$q$$$ answers. Each answer is "YES" or "NO" (case insensitive). Print "YES" if it is possible, that all employees on the corresponding day can access their compartments simultaneously.

Example
Input
3 10
2 3 2
6
1 5
2 1 10
2 2 9
2 5 6
3 1 7 8
4 1 2 3 4
Output
YES
YES
NO
NO
YES
NO