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.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.*;

public class Template implements Runnable {

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

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.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());
    }

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

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

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

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

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

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    long mod = (long) 1e9 + 7;
    int n;

    int[][] mul(int[][] a, int[][] b) {
        int[][] c = new int[n][n];
        int[][] transB = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                transB[i][j] = b[j][i];
            }
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    long mul = (long) a[i][k] * transB[j][k];
                    c[i][j] += mul % mod;
                    c[i][j] %= mod;
                }
            }
        }
        return c;
    }

    int[][] ident;

    int[][] binpow(int[][] a, long p) {
        if (p == 0) return ident;
        if (p % 2 == 0) {
            int[][] r = binpow(a, p / 2);
            return mul(r, r);
        } else {
            int[][] r = binpow(a, p - 1);
            return mul(a, r);
        }
    }

    void solve() throws IOException {
        n = readInt();

        ident = new int[n][n];
        for (int i = 0; i < n; i++) ident[i][i] = 1;

        long k = readLong();
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = readLong();
        }

        int[][] matr = new int[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                long xor = arr[i] ^ arr[j];
                int btcnt = Long.bitCount(xor);
                if (btcnt % 3 == 0) {
                    matr[i][j] = 1;
                }
            }
        }

        int[][] res = binpow(matr, k - 1);
        long ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                ans += res[i][j];
            }
        }
        ans %= mod;
        out.println(ans);


    }

}