HDU 5637 Transform

Problem Description

A list of  n integers are given. For an integer  x you can do the following operations:

+ let the binary representation of  x be  b31b30...b0¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯, you can flip one of the bits.
+ let  y be an integer in the list, you can change  x to  x⊕y, where  ⊕ means bitwise exclusive or operation.

There are several integer pairs  (S,T). For each pair, you need to answer the minimum operations needed to change  S to  T.

 

Input

There are multiple test cases. The first line of input contains an integer  T  (T≤20), indicating the number of test cases. For each test case:

The first line contains two integer  n and  m  (1≤n≤15,1≤m≤105) -- the number of integers given and the number of queries. The next line contains  nintegers  a1,a2,...,an  (1≤ai≤105), separated by a space.

In the next  m lines, each contains two integers  si and  ti  (1≤si,ti≤105), denoting a query.

 

Output

For each test cases, output an integer  S=(∑i=1mi⋅zi) mod (109+7), where  zi is the answer for  i-th query.

 

Sample Input

1 3 3 1 2 3 3 4 1 2 3 9

 

Sample Output

10

Hint

$3 \to 4$ (2 operations): $3 \to 7 \to 4$ $1 \to 2$ (1 operation): $1 \oplus 3 = 2$ $3 \to 9$ (2 operations): $3 \to 1 \to 9$

最近一直在做pat，做的人都水了，竟然想着暴力能过。。这题可以直接预处理处理所有的状态，然后直接o（1）回答就好了。

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