Mahmoud and Ehab and yet another xor task

题意翻译

- 给定一个有 $n$ 个数的序列 $\{a_n\}$。 - 有 $q$ 次形如 `l x` 的询问，每次询问要求输出前 $l$ 个数中，有多少子序列满足异或和为 $x$。 - $1\leq n,q\leq 10^5$， $0\leq a_i<2^{20}$。

题目描述

Ehab has an array $ a $ of $ n $ integers. He likes the [bitwise-xor operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) and he likes to bother Mahmoud so he came up with a problem. He gave Mahmoud $ q $ queries. In each of them, he gave Mahmoud 2 integers $ l $ and $ x $ , and asked him to find the number of subsequences of the first $ l $ elements of the array such that their bitwise-xor sum is $ x $ . Can you help Mahmoud answer the queries? A subsequence can contain elements that are not neighboring.

输入输出格式

输入格式

The first line contains integers $ n $ and $ q $ $ (1<=n,q<=10^{5}) $ , the number of elements in the array and the number of queries. The next line contains $ n $ integers $ a_{1} $ , $ a_{2} $ , $ ... $ , $ a_{n} $ $ (0<=a_{i}<2^{20}) $ , the elements of the array. The next $ q $ lines, each contains integers $ l $ and $ x $ $ (1<=l<=n $ , $ 0<=x<2^{20}) $ , representing the queries.

输出格式

For each query, output its answer modulo $ 10^{9}+7 $ in a newline.

输入输出样例

输入样例 #1

5 5
0 1 2 3 4
4 3
2 0
3 7
5 7
5 8

输出样例 #1

4
2
0
4
0

输入样例 #2

3 2
1 1 1
3 1
2 0

输出样例 #2

4
2

说明

The bitwise-xor sum of the empty set is 0 and the bitwise-xor sum of a set containing one element is that element itself.

题意翻译

- 给定一个有 $n$ 个数的序列 $\{a_n\}$。 - 有 $q$ 次形如 `l x` 的询问，每次询问要求输出前 $l$ 个数中，有多少子序列满足异或和为 $x$。 - $1\leq n,q\leq 10^5$， $0\leq a_i<2^{20}$。