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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Map.Entry;


import java.util.Random;
import java.util.TreeSet;

public final class CF_647_D1_B
{


	static boolean verb=true;
	static void log(Object X){if (verb) System.err.println(X);}
	static void log(Object[] X){if (verb) {for (Object U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");System.err.println("");}}
	static void logWln(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");}}
	static void log(int[] X,int L){if (verb) {for (int i=0;i<L;i++) System.err.print(X[i]+" ");System.err.println("");}}
	static void log(long[] X){if (verb) {for (long U:X) System.err.print(U+" ");System.err.println("");}}

	static void logWln(Object X){if (verb) System.err.print(X);}
	static void info(Object o){	System.out.println(o);}
	static void output(Object o){outputWln(""+o+"\n");	}
	static void outputFlush(Object o){try {out.write(""+ o+"\n");out.flush();} catch (Exception e) {}}
	static void outputWln(Object o){try {out.write(""+ o);} catch (Exception e) {}}


	static void logBin(int[] tm) {for (int x:tm) logWln(bin(8,x)+" ");log("");}

	static String bin(int L,int x) {
		String s=Integer.toBinaryString(x);
		while (s.length()<L) s="0"+s;
		return s;
	}

	static long powerMod(long b,long e,long m){
		long x=1;
		while (e>0) {
			if (e%2==1)
				x=(b*x)%m;
			b=(b*b)%m;
			e=e/2;
		}
		return x; 
	}


	static class Composite implements Comparable<Composite>{

		int val;
		int num;
		int idx;
		boolean natif;
		ArrayList<Composite> anc;


		public int compareTo(Composite X) {
			if (val!=X.val)
				return val-X.val;
			return idx-X.idx;
		}


		public Composite(int val, int num, int idx, boolean natif) {
			this.val = val;
			this.num = num;
			this.idx = idx;
			this.natif = natif;
			anc=new ArrayList<Composite>();
		}


		public String toString() {
			return "val:"+val+" num:"+num+" native:"+natif;
		}





	}

	// Global vars
	static BufferedWriter out;
	static InputReader reader;




	static long mod=1000000007;

	static void process() throws Exception {

		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader = new InputReader(System.in);

		int T=reader.readInt();
		int MX=2000001;
		int[] mem=new int[MX];
		int[] visited=new int[MX];
		int time=1;
		for (int t=0;t<T;t++) {
			//log("======reading for t:"+t);
			time++;
			int n=reader.readInt();
			int p=reader.readInt();
			int[] k=new int[n];
			for (int i=0;i<n;i++)
				k[i]=reader.readInt();

			long ans=0;
			if (p==1)
				ans=n%2;
			else {

				Arrays.parallelSort(k);
				//log(k);
				boolean empty=true;
				int left=0;
				long rightVal=0;
				for (int i=n-1;i>=0;i--) {
					if (empty) {
						left=k[i];
						//log("left:"+k[i]);
						empty=false;
					} else {
						int x=k[i];
						rightVal+=powerMod(p,x,mod);
						if (rightVal>=mod)
							rightVal-=mod;
						if (visited[x]<time) {
							visited[x]=time;
							mem[x]=0;
						}
						mem[x]++;
						while (mem[x]==p) {
							mem[x]=0;
							x++;
							if (visited[x]<time) {
								visited[x]=time;
								mem[x]=0;
							}
							mem[x]++;
						}
						if (left==x) {
							mem[x]=0;
							empty=true;
							rightVal=0;
						}
					}
				}

				if (!empty) {
					long A=powerMod(p,left,mod);
					ans=(A+mod-rightVal)%mod;

				}
			}
			output(ans);
		}
		try {
			out.close();
		} catch (Exception Ex) {
		}

	}





	public static void main(String[] args) throws Exception {
		process();

	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

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

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final String readString(int L) throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder(L);
			do {
				res.append((char) c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg = false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d = (char) c;
			// log("d:"+d);
			if (d == '-') {
				neg = true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			// log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

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

}