Problem:
Max Score: $400$ Points

Problem Statement

Sample testcase 3 has a mistake, so we erased this case and rejudged all solutions of this problem. (21:01)

Snuke got a sequence $a$ of length $n$ from AtCoder company. All elements in $a$ are distinct.

He made a sequence $b$, but actually, he is not remembered it.

However, he is remembered a few things about sequence $b$.

All elements in $b$ are distinct.

All elements in $b$ is in $a$.

$b_1 \oplus b_2 \oplus \cdots \oplus b_r = k$. ($r$ is length of sequence $b$) [$\oplus$ means XOR]

For example, if $a = { 1, 2, 3 }$ and $k = 1$, he can make $b = { 1 }, { 2, 3 }, { 3, 2 }$.

He wants to restore sequence $b$, but he says that there are too many ways and he can't restore it.
Please calculate the ways to make $b$ and help him.

Since the answer can be large, print the answer modulo $1,000,000,007$.

Input

The input is given from Standard Input in the following format:

$n \ k$
$a_1 \ a_2 \ \cdots \ a_n$

Output

Print the number of ways to make sequence $b$.

Print the answer modulo $1,000,000,007$.

Constraints

$1 \le n \le 100$

$1 \le a_i, k \le 255$

$i \neq j \Rightarrow a_i \neq a_j$

Subtasks

Subtask 1 [ $50$ points ]

$1 \le n \le 4$

Subtask 2 [ $170$ points ]

$1 \le n \le 20$

Subtask 3 [ $180$ points ]

There are no additional constraints.

Sample Input 1

3 1
1 2 3

Sample Output 1

3

You can make 3 patterns: $b = \{ 1 \}, \{ 2, 3 \}, \{ 3, 2 \}$

Sample Input 2

3 10
8 7 5

Sample Output 2

6

You can make 6 patterns: $b = \{ 5, 7, 8 \}, \{ 5, 8, 7 \}, \{ 7, 5, 8 \}, \{ 7, 8, 5 \}, \{ 8, 5, 7 \}, \{ 8, 7, 5 \}$.

Sample Input 4

25 127
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

Sample Output 4

235924722

Please output answer mod $1,000,000,007$.

writer: E869120

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <map>
#include <set>
#include <vector>
#include <stack>
#include <queue>
#include <bitset>
#include <algorithm>
#include <numeric>
#include <functional>
using namespace std;

#define Rep(b, e, i) for(int i = b; i <= e; i++)
#define Repr(e, b, i) for(int i = e; i >= b; i--)
#define rep(n, i) Rep(0, n-1, i)
#define repr(n, i) Repr(n-1, 0, i)
#define all(v) (v).begin(), (v).end()
#define pb(x) push_back(x)
#define uniq(x) (x).erase(unique(all(x)),(x).end())

typedef long long ll;
typedef pair<ll, ll> llP;
typedef pair<int, int> intP;
typedef std::priority_queue<int> IntPrioQueue; //Z->A
typedef std::priority_queue<int, std::vector<int>, std::greater<int> > IntReversePrioQueue; //A->Z

const int MAX = 256;
const double PI = 3.14159265358979323846;
const double EPS = 1e-12;
const int INF = 1<<29;
const int MOD = 1000000007;

int dp[MAX/2][MAX][MAX/2];
int ns[MAX/2];

void solve(void){
    int N, K;
    cin >> N >> K;
    rep(N, i) scanf("%d\n", &ns[i]);

    dp[0][0][0] = 1LL;
    rep(N, i) rep(MAX, j) rep(N, k) {
        dp[i+1][j][k] += dp[i][j][k];
        dp[i+1][j][k] %= MOD;
        dp[i+1][j^(ns[i])][k+1] += dp[i][j][k];
        dp[i+1][j^(ns[i])][k+1] %= MOD;
    }
    ll ans = 0LL;
    rep(N+1, k) {
        ll kaijyo = 1LL;
        Rep(1, k, i) {
            kaijyo *= (ll)i;
            kaijyo %= MOD;
        }
        ans += dp[N][K][k] * kaijyo;
        ans %= MOD;
    }
    
    cout << ans << endl;
}

int main(void){
  solve();
  //cout << "yui(*-v・)yui" << endl;
  return 0;
}