You are given n positive integers a_1, …, a_n, and an integer k ≥ 2. Count the number of pairs i, j such that 1 ≤ i < j ≤ n, and there exists an integer x such that a_i ⋅ a_j = x^k.

Input

The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 100).

The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10^5).

Output

Print a single integer — the number of suitable pairs.

Example

Input


6 3
1 3 9 8 24 1


Output


5

Note

In the sample case, the suitable pairs are:

  * a_1 ⋅ a_4 = 8 = 2^3;
  * a_1 ⋅ a_6 = 1 = 1^3;
  * a_2 ⋅ a_3 = 27 = 3^3;
  * a_3 ⋅ a_5 = 216 = 6^3;
  * a_4 ⋅ a_6 = 8 = 2^3.
import java.util.*;
import java.io.*;
import java.text.*;
public class Main{
    //SOLUTION BEGIN
    //Into the Hardware Mode
    void pre() throws Exception{}
    void solve(int TC)throws Exception{
        int n = ni(), k = ni(), mx = (int)1e5+1;
        long[] ar = new long[mx];
        int c = 0;
        HashSet<Long> set = new HashSet<>();
        for(int i = 1; i< mx; i++){
            long cur = 1;
            for(int j = 1; j<= k; j++)
                cur = Math.min(cur*i, (long)1e11);
            if(cur > 1e10)continue;
            ar[c++] = cur;
            set.add(cur);
        }
        long[] cnt = new long[mx];
        for(int i = 0; i< n; i++)cnt[ni()]++;
        long ans = 0;
        int[] spf = sieve(mx);
        for(int i = 1; i< mx; i++){
            long min = 1;
            int x = i;
            while(x > 1){
                int p = spf[x];
                int cc = 0;
                while(x%p == 0){
                    cc++;x/=p;
                }
                for(int j = 0; (j+cc)%k != 0; j++)
                    min = Math.min(mx, min*p);
            }
            if(cnt[i] == 0)continue;
            for(int j = 0; j < c && min*ar[j] < mx; j++){
                if(min*ar[j] <= i)continue;
                ans += cnt[i]*cnt[(int)(min*ar[j])];
            }
        }
        for(int i = 0; i< mx; i++)if(set.contains(i*(long)i))ans += (cnt[i]*cnt[i]-cnt[i])/2;
        pn(ans);
    }
    int[] sieve(int n){
        int[] spf = new int[n];
        spf[0] = spf[1] = 1;
        for(int i = 2; i< n; i++)if(spf[i] == 0)for(int j = i; j< n; j+=i)if(spf[j] == 0)spf[j] = i;
        return spf;
    }
    long pow(long a, long p){
        if(p <= 0)return 1;
        if(p == 1)return a;
        long x = pow(a, p/2);
        if(p%2 == 0)return Math.min(x*x, (long)1e6);
        return Math.min(x*x*a, (long)1e6);
    }
    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    void exit(boolean b){if(!b)System.exit(0);}
    long IINF = (long)1e18, mod = (long)1e9+7;
    final int INF = (int)1e9, MX = (int)2e6+5;
    DecimalFormat df = new DecimalFormat("0.0000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-7;
    static boolean multipleTC = false, memory = false, fileIO = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        if(fileIO){
            in = new FastReader("C:/users/user/desktop/inp.in");
            out = new PrintWriter("C:/users/user/desktop/out.out");
        }else {
            in = new FastReader();
            out = new PrintWriter(System.out);
        }
        //Solution Credits: Taranpreet Singh
        int T = (multipleTC)?ni():1;
        pre();
        for(int t = 1; t<= T; t++)solve(t);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    int find(int[] set, int u){return set[u] = (set[u] == u?u:find(set, set[u]));}
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}
 
    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }
 
        String next() throws Exception{
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    throw new Exception(e.toString());
                }
            }
            return st.nextToken();
        }
 
        String nextLine() throws Exception{
            String str = "";
            try{   
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }  
            return str;
        }
    }   
}