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 n integers 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
