Simon has a prime number x and an array of non-negative integers a1, a2, ..., an.

Simon loves fractions very much. Today he wrote out number <image> on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: <image>, where number t equals xa1 + a2 + ... + an. Now Simon wants to reduce the resulting fraction. 

Help him, find the greatest common divisor of numbers s and t. As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109 + 7).

Input

The first line contains two positive integers n and x (1 ≤ n ≤ 105, 2 ≤ x ≤ 109) — the size of the array and the prime number.

The second line contains n space-separated integers a1, a2, ..., an (0 ≤ a1 ≤ a2 ≤ ... ≤ an ≤ 109). 

Output

Print a single number — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

2 2
2 2


Output

8


Input

3 3
1 2 3


Output

27


Input

2 2
29 29


Output

73741817


Input

4 5
0 0 0 0


Output

1

Note

In the first sample <image>. Thus, the answer to the problem is 8.

In the second sample, <image>. The answer to the problem is 27, as 351 = 13·27, 729 = 27·27.

In the third sample the answer to the problem is 1073741824 mod 1000000007 = 73741817.

In the fourth sample <image>. Thus, the answer to the problem is 1.
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class cf359c {
  static FastIO in = new FastIO(), out = in;

  static long mod = (long)1e9 + 7;
  public static void main(String[] args) {
    long n = in.nextLong();
    long x = in.nextLong();
    long[] v = new long[(int)n];
    long sum = 0;
    for(int i=0; i<n; i++)
      sum += v[i]=in.nextLong();
    Cluster cluster = new Cluster();
    for(long z : v) cluster.add(sum-z, 1);
    long ret = 0;
    while(true) {
      long a = cluster.min();
      long b = cluster.get(a);
      if(b%x == 0) {
        cluster.remove(a, b);
        cluster.add(a+1, b/x);
      }
      else {
        ret = a;
        break;
      }
    }
    if(ret > sum) ret = sum;
    out.println(pow(x,ret));
    out.close();
  }
  static long pow(long x, long p) {
    if(p == 0) return 1;
    long v = pow(x,p>>1);
    v = (v*v)%mod;
    if((p&1)==1) v=(v*x)%mod;
    return v;
  }
  
  static class Cluster {
    TreeMap<Long, Long> map = new TreeMap<Long,Long>();
    
    long min() {
      return map.firstKey();
    }
    void add(long x, long v) {
      set(x, get(x)+v);
    }
    void remove(long x, long v) {
      set(x, get(x)-v);
    }
    void set(long x, long v) {
      if(v == 0) map.remove(x);
      else map.put(x, v);
    }
    long get(long x) {
      if(map.containsKey(x)) return map.get(x);
      return 0;
    }
    public String toString() {
      return map.toString();
    }
  }

  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;

    public FastIO() {
      this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }

    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch (Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }

    public int numTokens() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }

    public String next() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }

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

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

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