#P959F. Mahmoud and Ehab and yet another xor task
Mahmoud and Ehab and yet another xor task
Description
Ehab has an array a of n integers. He likes the bitwise-xor operation 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.
The first line contains integers n and q (1 ≤ n, q ≤ 105), the number of elements in the array and the number of queries.
The next line contains n integers a1, a2, ..., an (0 ≤ ai < 220), the elements of the array.
The next q lines, each contains integers l and x (1 ≤ l ≤ n, 0 ≤ x < 220), representing the queries.
For each query, output its answer modulo 109 + 7 in a newline.
Input
The first line contains integers n and q (1 ≤ n, q ≤ 105), the number of elements in the array and the number of queries.
The next line contains n integers a1, a2, ..., an (0 ≤ ai < 220), the elements of the array.
The next q lines, each contains integers l and x (1 ≤ l ≤ n, 0 ≤ x < 220), representing the queries.
Output
For each query, output its answer modulo 109 + 7 in a newline.
Samples
5 5
0 1 2 3 4
4 3
2 0
3 7
5 7
5 8
4
2
0
4
0
3 2
1 1 1
3 1
2 0
4
2
Note
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.