# 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.