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.

<image> 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 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 4 ⋅ 10^5) — the number of doors and compartments respectively.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ m, ∑{a_i} ≤ m) — the corresponding widths of the doors.

The third line contains a single integer q (1 ≤ q ≤ 2 ⋅ 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, ..., w_{c_k} (1 ≤ c_k ≤ 2 ⋅ 10^5, 1 ≤ w_1 < w_2 < ... < w_{c_k} ≤ m) — the number of employees who will come on the k-th day, and their indices in ascending order.

It's guaranteed that ∑{c_k} doesn't exceed 2 ⋅ 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

Source: codeforces | Difficulty: UNKNOWN_DIFFICULTY
Tags: Sorting


Solutions: