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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
class Solve{
    int N,K;
    int[] a;
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Read();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        long[,,] dp = new long[N,N+1,256];
        long[] fact = new long[N+1];
        long count = 0;
        for(int i=0;i<N;i++){
            for(int j=0;j<N+1;j++){
                for(int k=0;k<256;k++){
                    if(j == 0){
                        if(k == 0){
                            dp[i,j,k] = 1;
                        }
                        else{
                            dp[i,j,k] = 0;
                        }
                    }
                    else if(i == 0){
                        if(k == a[0] && j == 1){
                            dp[i,j,k] = 1;
                        }
                        else{
                            dp[i,j,k] = 0;
                        }
                    }
                    else{
                        dp[i,j,k] = (dp[i-1,j,k] + dp[i-1,j-1,k^a[i]]) % Define.mod;
                    }
                }
            }
        }
        for(int i=0;i<N+1;i++){
            if(i == 0){
                fact[i] = 1;
            }
            else{
                fact[i] = (fact[i-1] * i) % Define.mod;
            }
        }
        for(int i=1;i<N+1;i++){
            count = (count + (dp[N-1,i,K] * fact[i] % Define.mod)) % Define.mod; 
        }
        sb.Append(count+"\n");
    }
    void Read(){
        string[] str = Console.ReadLine().Split(' ');
        N = int.Parse(str[0]);
        K = int.Parse(str[1]);
        str = Console.ReadLine().Split(' ');
        a = new int[N];
        for(int i=0;i<N;i++){
            a[i] = int.Parse(str[i]);
        }
    }    
}
public static class Define{
    public const long mod = 1000000007;
}