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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
struct Matrix {
  int n, m;
  long long d[100][100];
  Matrix(int a, int b) {
    n = a, m = b;
    memset(d, 0, sizeof(d));
  }
  void Copy(int *tmp) {
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        d[i][j] = *tmp;
        tmp++;
      }
  }
  friend Matrix operator*(const Matrix &a, const Matrix &b) {
    Matrix c(a.n, b.m);
    for (int i = 0; i < a.n; i++)
      for (int j = 0; j < b.m; j++) {
        long long tmp = 0;
        for (int k = 0; k < a.m; k++) {
          tmp += a.d[i][k] * b.d[k][j] % mod;
          if (tmp >= mod) tmp -= mod;
        }
        c.d[i][j] = tmp;
      }
    return c;
  }
};
int n;
long long k, a[110];
int getnum(long long x) {
  int cnt = 0;
  while (x) {
    cnt += x & 1;
    x >>= 1;
  }
  return cnt % 3;
}
void solve(long long m) {
  Matrix A(100, 100);
  for (int i = 0; i < n; i++) A.d[i][i] = 1;
  Matrix B(100, 100);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      if (!getnum(a[i] ^ a[j])) B.d[i][j] = 1;
  while (m) {
    if (m & 1) A = A * B;
    B = B * B;
    m = m >> 1;
  }
  long long cnt = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      cnt = cnt + A.d[i][j];
      if (cnt >= mod) cnt -= mod;
    }
  printf("%I64d\n", cnt);
  return;
}
int main() {
  while (scanf("%d %I64d", &n, &k) != EOF) {
    for (int i = 0; i < n; i++) scanf("%I64d", &a[i]);
    if (k == 1) {
      printf("%d\n", n);
      continue;
    }
    solve(k - 1);
  }
  return 0;
}