Polycarp loves geometric progressions very much. Since he was only three years old, he loves only the progressions of length three. He also has a favorite integer k and a sequence a, consisting of n integers.

He wants to know how many subsequences of length three can be selected from a, so that they form a geometric progression with common ratio k.

A subsequence of length three is a combination of three such indexes i1, i2, i3, that 1 ≤ i1 < i2 < i3 ≤ n. That is, a subsequence of length three are such groups of three elements that are not necessarily consecutive in the sequence, but their indexes are strictly increasing.

A geometric progression with common ratio k is a sequence of numbers of the form b·k0, b·k1, ..., b·kr - 1.

Polycarp is only three years old, so he can not calculate this number himself. Help him to do it.

Input

The first line of the input contains two integers, n and k (1 ≤ n, k ≤ 2·105), showing how many numbers Polycarp's sequence has and his favorite number.

The second line contains n integers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — elements of the sequence.

Output

Output a single number — the number of ways to choose a subsequence of length three, such that it forms a geometric progression with a common ratio k.

Examples

Input

5 2
1 1 2 2 4


Output

4

Input

3 1
1 1 1


Output

1

Input

10 3
1 2 6 2 3 6 9 18 3 9


Output

6

Note

In the first sample test the answer is four, as any of the two 1s can be chosen as the first element, the second element can be any of the 2s, and the third element of the subsequence must be equal to 4.
import java.io.*;
import java.util.*;

public class C {
    public static void solution(BufferedReader reader, PrintWriter out)
            throws IOException {
        In in = new In(reader);
        int n = in.nextInt(), k = in.nextInt();
        TreeMap<Integer, ArrayList<Integer>> a = new TreeMap<Integer, ArrayList<Integer>>();
        for (int i = 0; i < n; i++) {
            int ai = in.nextInt();
            if (!a.containsKey(ai))
                a.put(ai, new ArrayList<Integer>());
            a.get(ai).add(i);
        }
        int max = 1000000000 / k / k;
        long cnt = 0;
        for (Integer a1 : a.keySet())
            if (Math.abs(a1) <= max) {
                int a2 = a1 * k, a3 = a2 * k;
                if (a.containsKey(a2) && a.containsKey(a3))
                    for (int i : a.get(a2)) {
                        long a1cnt = lower(i, a.get(a1));
                        long a3cnt = higher(i, a.get(a3));
                        cnt += a1cnt * a3cnt;
                    }
            }
        out.println(cnt);
    }

    private static int higher(int num, ArrayList<Integer> list) {
        if (list.get(list.size() - 1) <= num)
            return 0;
        int i = -1, j = list.size() - 1;
        while (i + 1 < j) {
            int mid = (i + j) / 2;
            if (list.get(mid) <= num)
                i = mid;
            else
                j = mid;
        }
        return list.size() - j;
    }

    private static int lower(int num, ArrayList<Integer> list) {
        if (list.get(0) >= num)
            return 0;
        int i = 0, j = list.size();
        while (i + 1 < j) {
            int mid = (i + j) / 2;
            if (list.get(mid) < num)
                i = mid;
            else
                j = mid;
        }
        return i + 1;
    }

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(
                new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(System.out)));
        solution(reader, out);
        out.close();
    }

    protected static class In {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public In(BufferedReader reader) {
            this.reader = reader;
        }

        public String next() throws IOException {
            while (!tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

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

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

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