Problem: You are given n integers a1, a2, ..., an.

A sequence of integers x1, x2, ..., xk is called a "xor-sequence" if for every 1 ≤ i ≤ k - 1 the number of ones in the binary representation of the number xi <image> xi + 1's is a multiple of 3 and <image> for all 1 ≤ i ≤ k. The symbol <image> is used for the binary exclusive or operation.

How many "xor-sequences" of length k exist? Output the answer modulo 109 + 7.

Note if a = [1, 1] and k = 1 then the answer is 2, because you should consider the ones from a as different.

Input

The first line contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 1018) — the number of given integers and the length of the "xor-sequences".

The second line contains n integers ai (0 ≤ ai ≤ 1018).

Output

Print the only integer c — the number of "xor-sequences" of length k modulo 109 + 7.

Examples

Input

5 2
15 1 2 4 8


Output

13


Input

5 1
15 1 2 4 8


Output

5

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class E implements Runnable {

    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private BufferedReader in;
    private PrintWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    private void init() throws FileNotFoundException {
        Locale.setDefault(Locale.US);
        String fileName = "";
        if (ONLINE_JUDGE && fileName.isEmpty()) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            if (fileName.isEmpty()) {
                in = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            } else {
                in = new BufferedReader(new FileReader(fileName + ".in"));
                out = new PrintWriter(fileName + ".out");
            }
        }
    }

    String readString() {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() {
        return Integer.parseInt(readString());
    }

    long readLong() {
        return Long.parseLong(readString());
    }

    double readDouble() {
        return Double.parseDouble(readString());
    }

    int[] readIntArray(int size) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = readInt();
        }
        return a;
    }

    public static void main(String[] args) {
        //new Thread(null, new _Solution(), "", 128 * (1L << 20)).start();
        new E().run();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    @Override
    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            init();
            solve();
            out.close();
            time();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    final int MOD = 1000 * 1000 * 1000 + 7;

    private int[][] matrixMultiplication(int[][] matrixA, int[][] matrixB) {
        int size = matrixA.length;
        int[][] result = new int[size][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < size; j++) {
                for (int k = 0; k < size; k++) {
                    result[i][j] = (int) (((long) result[i][j] + (long) matrixA[i][k] * matrixB[k][j]) % MOD);
                }
            }
        }
        return result;
    }

    private int[][] binPow(int[][] matrix, long power) {
        if (power == 1) {
            return matrix;
        }
        if (power % 2 == 0) {
            int[][] matrixHalf = binPow(matrix, power / 2);
            return matrixMultiplication(matrixHalf, matrixHalf);
        } else {
            return matrixMultiplication(matrix, binPow(matrix, power - 1));
        }
    }

    private void solve() throws IOException {
        int n = readInt();
        long k = readLong();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = readLong();
        }

        if (k == 1) {
            out.println(n);
            return;
        }

        int[][] matrix = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (Long.bitCount(a[i] ^ a[j]) % 3 == 0) {
                    matrix[i][j] = 1;
                }
            }
        }

        matrix = binPow(matrix, k - 1);
        long ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++)
                ans = (ans + matrix[i][j]) % MOD;
        }
        out.println(ans);
    }
}