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 $11$.
# cook your dish here
t=int(input())
for i in range(t):
 n,q=list(map(int,input().split()))
 a=list(map(int, input().split()))
 even,odd=0,0
 for j in range(n):
  count=(bin(a[j]).count("1"))
  if count%2==0: 
   even = even + 1
  else:   
   odd = odd + 1

 for j in range(q):
  m=int(input())
  g=bin(m).count("1")
  a,b=even,odd
  if g%2==0:
   a,b=even,odd
  else: 
   a,b=odd,even
  print(a,b)

# cook your dish here
t=int(input())
for i in range(t):
 n,q=list(map(int,input().split()))
 a=list(map(int, input().split()))
 even,odd=0,0
 for j in range(n):
  count=(bin(a[j]).count("1"))
  if count%2==0: 
   even = even + 1
  else:   
   odd = odd + 1

 for j in range(q):
  m=int(input())
  g=bin(m).count("1")
  a,b=even,odd
  if g%2==0:
   a,b=even,odd
  else: 
   a,b=odd,even
  print(a,b)
