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.

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, ..., a_n (0 ≤ a_i < 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.

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.

Mahmoud and Ehab and yet another xor task

Examples