Johnny has just found the new, great tutorial: "How to become a grandmaster?". The tutorial tells many strange and unexpected for Johnny things, such as you have to be patient or that very important is solving many harder and harder problems. 

The boy has found an online judge with tasks divided by topics they cover. He has picked p^{k_i} problems from i-th category (p is his favorite number). He wants to solve them in two weeks (the patience condition is too hard for Johnny, so for simplicity, he looks only at easy tasks, which can be solved in such a period). Now our future grandmaster has to decide which topics to cover first and which the second week. Help him assign topics in such a way, that workload is balanced.

Formally, given n numbers p^{k_i}, the boy wants to divide them into two disjoint sets, minimizing the absolute difference between sums of numbers in each set. Find the minimal absolute difference. Output the result modulo 10^{9}+7.

Input

Input consists of multiple test cases. The first line contains one integer t (1 ≤ t ≤ 10^5) — the number of test cases. Each test case is described as follows:

The first line contains two integers n and p (1 ≤ n, p ≤ 10^6). The second line contains n integers k_i (0 ≤ k_i ≤ 10^6).

The sum of n over all test cases doesn't exceed 10^6.

Output

Output one integer — the reminder of division the answer by 1 000 000 007.

Example

Input


4
5 2
2 3 4 4 3
3 1
2 10 1000
4 5
0 1 1 100
1 8
89


Output


4
1
146981438
747093407

Note

You have to minimize the difference, not it's remainder. For example, if the minimum difference is equal to 2, but there is also a distribution where the difference is 10^9 + 8, then the answer is 2, not 1.

In the first test case of the example, there're the following numbers: 4, 8, 16, 16, and 8. We can divide them into such two sets: {4, 8, 16} and {8, 16}. Then the difference between the sums of numbers in sets would be 4.
import java.io.*;
import java.util.*;

/*
polyakoff
*/

public class Main {

    static FastReader in;
    static PrintWriter out;
    static Random rand = new Random();
    static final int oo = (int) 2e9;
    static final long OO = (long) 4e18;
    static final int MOD = (int) 1e9 + 7;

    static long pow(long a, long b) {
        long res = 1;
        while (b != 0) {
            if ((b & 1) == 1)
                res = (res * a) % MOD;
            a = (a * a) % MOD;
            b >>= 1;
        }
        return res;
    }

    static long add(long a, long b) {
        long res = (a + b) % MOD;
        if (res < 0)
            res += MOD;
        return res;
    }

    static void solve() {
        int n = in.nextInt();
        int p = in.nextInt();

        int[] k = new int[n];
        for (int i = 0; i < n; i++)
            k[i] = in.nextInt();

        if (p == 1) {
            out.println(n % 2);
            return;
        }

        Arrays.sort(k);
        for (int i = 0; i < n / 2; i++) {
            int j = n - 1 - i;
            k[i] ^= k[j];
            k[j] ^= k[i];
            k[i] ^= k[j];
        }

        long dif = 0;
        for (int i = 0; i < n; i++) {
            int r = i + 1;
            while (r < n && k[i] == k[r])
                r++;

            if (r == n) {
                if ((r - i) % 2 == 1)
                    dif = pow(p, k[i]);
                break;
            }

            if ((r - i) % 2 == 0) {
                i = r - 1;
                continue;
            }

            dif = pow(p, k[i]);

            long m = 1;
            int delta = k[i] - k[r];
            while (m < n && delta > 0) {
                m *= p;
                delta--;
            }

            int j = r;
            int last = k[r];
            for (; j < Math.min(r + m, n); j++) {
                if (k[j] < last) {
                    long dm = r + m - j;
                    delta = k[j - 1] - k[j];
                    while (dm < n && delta > 0) {
                        dm *= p;
                        delta--;
                    }
                    m = j - r + dm;
                    last = k[j];
                }
                dif = add(dif, -pow(p, k[j]));
            }

            i = j - 1;

        }

        out.println(dif);



    }

    public static void main(String[] args) throws FileNotFoundException {
        in = new FastReader(System.in);
//        in = new FastReader(new FileInputStream("sometext.txt"));
        out = new PrintWriter(System.out);
//        out = new PrintWriter(new FileOutputStream("output.txt"));

        int T = 1;
        T = in.nextInt();
        while (T-- > 0)
            solve();

//        Thread thread = new Thread(null, () -> {
//            solve();
//        }, "Main", 1 << 28);
//        thread.start();
//        try {
//            thread.join();
//        } catch (InterruptedException e) {
//            e.printStackTrace();
//        }

//        out.flush();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        Integer nextInt() {
            return Integer.parseInt(next());
        }

        Long nextLong() {
            return Long.parseLong(next());
        }

        Double nextDouble() {
            return Double.parseDouble(next());
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }
    }

    static void dbg(Object... args) {
        for (Object arg : args)
            out.print(arg + " ");
        out.println();
    }

}