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 java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.util.ArrayDeque;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        static final long MODULO = (long) (1e9 + 7);

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int Q = in.nextInt();
            int[] a = in.nextIntArray(n);
            TaskF.Query[] queries = new TaskF.Query[Q];
            for (int q = 0; q < Q; ++q) {
                queries[q] = new TaskF.Query(in.nextInt() - 1, in.nextInt(), q);
            }
            Arrays.sort(queries, Comparator.comparingInt(o -> o.l));
            ArrayDeque<TaskF.Query> deque = new ArrayDeque<>();
            for (TaskF.Query q : queries) deque.add(q);
            ArrayList<Integer> gaussian = new ArrayList<>();
            long ret = 1;
            long[] ans = new long[Q];
            for (int i = 0; i < n; ++i) {
                int cur = a[i];
                for (Integer v : gaussian)
                    if ((cur ^ v) < cur)
                        cur ^= v;
                if (cur != 0) {
                    gaussian.add(cur);
                    Collections.sort(gaussian, Collections.reverseOrder());
                } else {
                    ret *= 2;
                    if (ret >= MODULO)
                        ret %= MODULO;
                }
                while (!deque.isEmpty() && deque.peek().l == i) {
                    TaskF.Query query = deque.pollFirst();
                    cur = query.x;
                    for (Integer v : gaussian)
                        if ((cur ^ v) < cur)
                            cur ^= v;
                    if (cur == 0)
                        ans[query.idx] = ret;
                }
            }
            ArrayUtils.printArray(out, ans);
        }

        static class Query {
            int l;
            int x;
            int idx;

            public Query(int l, int x, int idx) {
                this.l = l;
                this.x = x;
                this.idx = idx;
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }

    static class ArrayUtils {
        public static void printArray(PrintWriter out, long[] array) {
            if (array.length == 0) return;
            for (int i = 0; i < array.length; i++) {
                if (i != 0) out.print(" ");
                out.print(array[i]);
            }
            out.println();
        }

    }
}

