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.

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.

Examples

Input

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


Output

4
2
0
4
0


Input

3 2
1 1 1
3 1
2 0


Output

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.
import sys
range = xrange
input = raw_input

MOD = 10**9 + 7
inp = [int(x) for x in sys.stdin.read().split()]; ii = 0

n = inp[ii]; ii += 1
q = inp[ii]; ii += 1

A = inp[ii: ii + n]; ii += n

zeros = [1]
Abase = []
base = []
for i in range(n):
    a = A[i]
    for b in base:
        if a ^ b < a:
            a ^= b
    if a:
        base = list(base)
        base.append(a)
        base.sort(reverse = True)
        zeros.append(zeros[-1])
    else:
        zeros.append(zeros[-1] * 2 % MOD)
    Abase.append(base)

out = []
for _ in range(q):
    l = inp[ii] - 1; ii += 1
    x = inp[ii]; ii += 1

    for b in Abase[l]:
        if x ^ b < x:
            x ^= b

    out.append(0 if x else zeros[l + 1])

print '\n'.join(str(x) for x in out)
