Transform（HDU-5637）

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 , 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 , 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

题意：t 组数据，每组给出 n 个数与 m 组询问，每组询问有 s、t 两个数，对于数 s 现给出两种变换，一种是改变 s 二进制位的某一位，即 0 变 1 或 1 变 0，另一种是让 s 从给出 n 个数当中的任意一个做异或运算，问从 s 到 t 最少要经过几步变换，最后输出每组的组号 i 与该组答案 zi 的和然后模 1E9+7

思路：假设 s^x^y^z^w^...^q=t 是最小操作次数，由于其等价于 0^x^y^z^w^...^q=s^t，因此只需要根据所给的 n 个数将 1E5 范围内的所有步数求出来存到 res[] 数组中，最后根据 s、t 的值直接可以得到 res[s^t] 然后进行计算即可。

Source Program

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