Chef wants to organize a contest. Predicting difficulty levels of the problems can be a daunting task. Chef wants his contests to be balanced in terms of difficulty levels of the problems.
Assume a contest had total P participants. A problem that was solved by at least half of the participants (i.e. P / 2 (integer division)) is said to be cakewalk difficulty. A problem solved by at max P / 10 (integer division) participants is categorized to be a hard difficulty.
Chef wants the contest to be balanced. According to him, a balanced contest must have exactly 1 cakewalk and exactly 2 hard problems. You are given the description of N problems and the number of participants solving those problems. Can you tell whether the contest was balanced or not?

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
The first line of each test case contains two space separated integers, N, P denoting the number of problems, number of participants respectively.
The second line contains N space separated integers, i-th of which denotes number of participants solving the i-th problem.

-----Output-----
For each test case, output "yes" or "no" (without quotes) denoting whether the contest is balanced or not.

-----Constraints-----
- 1 ≤ T, N ≤ 500 
- 1 ≤ P ≤ 108 
- 1 ≤ Number of participants solving a problem ≤ P

-----Subtasks-----
- Subtask #1 (40 points): P is a multiple of 10
- Subtask #2 (60 points): Original constraints

-----Example-----
Input
6
3 100
10 1 100
3 100
11 1 100
3 100
10 1 10
3 100
10 1 50
4 100
50 50 50 50
4 100
1 1 1 1

Output
yes
no
no
yes
no
no

-----Explanation-----
Example case 1.: The problems are of hard, hard and cakewalk difficulty. There is 1 cakewalk and 2 hard problems, so the contest is balanced.
Example case 2.: The second problem is hard and the third is cakewalk. There is 1 cakewalk and 1 hard problem, so the contest is not balanced.
Example case 3.: All the three problems are hard. So the contest is not balanced.
Example case 4.: The problems are of hard, hard, cakewalk difficulty. The contest is balanced.
Example case 5.: All the problems are cakewalk. The contest is not balanced.
Example case 6.: All the problems are hard. The contest is not balanced.

```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 = 'def ishard(participants , studentswhosolved):\n if studentswhosolved <= int(participants/10):\n  return True\n else :\n  return False\n\ndef iscakewalk(participants , studentswhosolved):\n if studentswhosolved >= int(participants/2):\n  return True\n else :\n  return False\n\nfor t in range(int(input())):\n n, p = list(map(int, input().split()))\n cakwalkproblems = 0\n hardproblems = 0\n numberlist = list(map(int,input().split()))\n for _ in range(n):\n  if ishard(p , numberlist[_]):\n   hardproblems+=1\n  elif iscakewalk(p , numberlist[_]) :\n   cakwalkproblems+=1\n if cakwalkproblems == 1 and hardproblems == 2 :\n  print("yes")\n else :\n  print("no")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13511