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.util.*;
import java.math.*;



public class Task{
    public static void main(String[] args) throws IOException{
        new Task().run();
    }
    
    StreamTokenizer in; 
    Scanner ins;
    PrintWriter out;

    int nextInt() throws IOException{
        in.nextToken();      
        return (int)in.nval;
    }
    
    long nextLong() throws IOException{
        in.nextToken();      
        return (long)in.nval;
    }
    
    double nextDouble() throws IOException{
        in.nextToken();      
        return in.nval;
    }
    
    char nextChar() throws IOException{
        in.nextToken();
        return (char)in.ttype;
    }
    
    String nextString() throws IOException{
        in.nextToken();
        return in.sval;
    }
     
    private static final String INPUT = "g.in";
    
    private static final long MOD = 1000000007;
    int n;
    long p;
    long a[];
    int subCoef = 0;
    void run() throws IOException{        
        in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        ins = new Scanner(System.in);        
        out = new PrintWriter(System.out);
        try{
            if(System.getProperty("xDx")!=null){
                in = new StreamTokenizer(new BufferedReader(new FileReader("input.txt")));
                ins = new Scanner(new FileReader("input.txt"));
                out = new PrintWriter(new FileWriter("output.txt"));
            }else{
    //                in = new StreamTokenizer(new BufferedReader(new FileReader(INPUT)));
    //                ins = new Scanner(new FileReader(INPUT));
    //                out = new PrintWriter(System.out);
            }
        }catch(Exception e){
    //            in = new StreamTokenizer(new BufferedReader(new FileReader(INPUT)));
    //            ins = new Scanner(new FileReader(INPUT));
    //            out = new PrintWriter(System.out);
        }

        n = nextInt();
        p = nextInt();
        a = new long[n];
        long max = 0;
        long stAnsw;
        long sum = 0;
        for(int i = 0; i < n; i++){
            a[i] = nextInt();
            max = Math.max(a[i], max);
            sum += a[i];
        }
        Arrays.sort(a);
        stAnsw = sum - max;
        for(int i = 0; i < n; i++){
            a[i] = max - a[i];            
        }
        
        boolean isEnd = false;               
        while(!isEnd){            
            int tmpPos = findPos();
            int tmpCount = n - tmpPos;
            n = tmpPos;            
            if(tmpCount % p == 0){
                tmpCount /= p;
                stAnsw++;
                subCoef++;
                for(int i = 0; i < tmpCount; i++){
                    a[n++] = subCoef;
                }
            }else{
                isEnd = true;
            }                        
        }
        
        stAnsw = Math.min(stAnsw, sum);
        out.print(pow(p, stAnsw));          
        out.close();

    }   
    
    long pow(long x, long st){
        if(st == 0){
            return 1;
        }
        long tmp = pow(x, st/2);
        tmp = (tmp*tmp) % MOD;
        if(st%2 == 1){
            tmp = (tmp*x) % MOD;
        }
        return tmp;
    }
    int findPos(){
        int l = 0, r = n - 1;
        int res = n - 1;
        while(l <= r){
            int mid = (l + r)/2;
            long x = a[mid] - subCoef;
            if(x > 0){
                l = mid + 1;                
            }else if(x == 0){
                r = mid - 1;
                res = Math.min(res, mid);
            }else{
                r = mid - 1;
            }
        }
        return res;
    }
}