A sophomore Computer Science student is frustrated with boring college lectures. Professor X agreed to give him some questions; if the student answers all questions correctly, then minimum attendance criteria will not apply to him.
Professor X chooses a sequence $A_1, A_2, \ldots, A_N$ and asks $Q$ queries. In each query, the student is given an integer $P$; he has to construct a sequence $B_1, B_2, \ldots, B_N$, where $P \oplus A_i = B_i$ for each valid $i$ ($\oplus$ denotes bitwise XOR), and then he has to find the number of elements of this sequence which have an even number of $1$-s in the binary representation and the number of elements with an odd number of $1$-s in the binary representation. Help him answer the queries.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $Q$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- $Q$ lines follow. Each of these lines contains a single integer $P$ describing a query.

-----Output-----
For each query, print a single line containing two space-separated integers ― the number of elements with an even number of $1$-s and the number of elements with an odd number of $1$-s in the binary representation.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, Q \le 10^5$
- $ T \cdot (N+Q) \leq 4 \cdot 10^6 $
- $1 \le A_i \le 10^8$ for each valid $i$
- $1 \le P \le 10^5$
The input/output is quite large, please use fast reading and writing methods.

-----Subtasks-----
Subtask #1 (30 points): $N, Q \le 1,000$
Subtask #2 (70 points): original constraints

-----Example Input-----
1
6 1
4 2 15 9 8 8
3

-----Example Output-----
2 4

-----Explanation-----
Example case 1: The elements of the sequence $B$ are $P \oplus 4 = 7$, $P \oplus 2 = 1$, $P \oplus 15 = 12$, $P \oplus 9 = 10$, $P \oplus 8 = 11$ and $P \oplus 8 = 11$. The elements which have an even number of $1$-s in the binary representation are $12$ and $10$, while the elements with an odd number of $1$-s are $7$, $1$, $11$ and $11$.

```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 = 'from sys import stdin,stdout\ndef main():\n t=int(stdin.readline())\n for i in range(t):\n  list2=[]\n  n,q=map(int,stdin.readline().split()) \n  a=list(map(int,stdin.readline().split()))\n  for i in range(len(a)):                     \n   list2.append((bin(a[i])).count("1"))\n  for i in range(q):                          \n   b=0\n   b=int(stdin.readline())\n   e=0\n   o=0\n   for i in range(len(list2)):\n    if((list2[i]%2)==0):\n     e+=1\n    else:\n     o+=1\n   e1=0\n   e1=bin(b).count("1")\n   if(e1%2==0):\n    print(e,end=" ")\n    print(o)\n   else:\n    print(o,end=" ")\n    print(e)\ndef __starting_point():\n main()\n#a=5\n#str1=""\n#str1+=bin(a)\n#print(str1[2:])\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14577