Alice lives on a line. Today, she will travel to some place in a mysterious vehicle.
Initially, the distance between Alice and her destination is D. When she input a number x to the vehicle, it will travel in the direction of the destination by a distance of x if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than x.
Alice made a list of N numbers. The i-th number in this list is d_i. She will insert these numbers to the vehicle one by one.
However, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after N moves.
She has Q plans to do this, as follows:
 - Rewrite only the q_i-th number in the list with some integer so that Alice will not reach the destination.
Write a program to determine whether each plan is feasible.

-----Constraints-----
 - 1≤ N ≤ 5*10^5
 - 1≤ Q ≤ 5*10^5
 - 1≤ D ≤ 10^9
 - 1≤ d_i ≤ 10^9(1≤i≤N)
 - 1≤ q_i ≤ N(1≤i≤Q)
 - D and each d_i are integers.

-----Input-----
Input is given from Standard Input in the following format:
N D
d_1 d_2 ... d_N
Q
q_1 q_2 ... q_Q

-----Output-----
Print Q lines. The i-th line should contain YES if the i-th plan is feasible, and NO otherwise.

-----Sample Input-----
4 10
3 4 3 3
2
4 3

-----Sample Output-----
NO
YES

For the first plan, Alice will already arrive at the destination by the first three moves, and therefore the answer is NO.
For the second plan, rewriting the third number in the list with 5 will prevent Alice from reaching the destination as shown in the following figure, and thus the answer is YES.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\n\n"""\n後ろから、到達不可能距離の集合を見ていきたい。\n集合を持つと厳しいが、最小値だけ持っておけばよい。\n"""\n\nN,dist = map(int,input().split())\nD = [int(x) for x in input().split()]\n\n# 各ターンの出発位置\nstart_dist = [dist]\nfor d in D:\n    x = start_dist[-1]\n    y = x-d if x > d else d - x\n    start_dist.append(x if x < y else y)\n\nng_dist = [None] * (N+1)\nng_dist[N] = 1\n\nfor i,d in enumerate(D[::-1]):\n    x = ng_dist[N-i]\n    y = x if x <= d//2 else x + d\n    ng_dist[N-i-1] = y\n\ninput()\nQ = [int(x) for x in input().split()]\n\nanswer = [\'YES\' if ng_dist[d] <= start_dist[d-1] else \'NO\' for d in Q]\n\nprint(\'\\n\'.join(answer))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13445