CodeForces - 1513B AND Sequences

B. AND Sequences
time limit per test: 2 seconds
memory limit per test: 256 megabytes

A sequence of n non-negative integers (n≥2) a1,a2,…,an is called good if for all i from 1 to n−1 the following condition holds true:
a1&a2&…&ai=ai+1&ai+2&…&an,a_1 \& a_2 \& … \& a_i = a_{i+1} \& a_{i+2} \& … \&a_n, a1&a2&…&ai=ai+1&ai+2&…&an,
where & denotes the bitwise AND operation.

You are given an array a of size n (n≥2). Find the number of permutations p of numbers ranging from 1 to n, for which the sequence ap1,ap2,...,apna_{p1}, a_{p2}, ... ,a_{pn}ap1,ap2,...,apn is good. Since this number can be large, output it modulo 109+710^9+7109+7.

Input
The first line contains a single integer t (1≤t≤10⁴), denoting the number of test cases.

The first line of each test case contains a single integer n (2≤n≤2⋅10⁵) — the size of the array.

The second line of each test case contains n integers a1,a2,…,an (0≤ai≤10⁹) — the elements of the array.

It is guaranteed that the sum of n over all test cases doesn’t exceed 2⋅10⁵.

Output
Output t lines, where the i-th line contains the number of good permutations in the i-th test case modulo 10⁹+7.

Example
input
4
3
1 1 1
5
1 2 3 4 5
5
0 2 0 3 0
4
1 3 5 1
output
6
0
36
4
Note
In the first test case, since all the numbers are equal, whatever permutation we take, the sequence is good. There are a total of 6 permutations possible with numbers from 1 to 3: [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], [3,2,1].

In the second test case, it can be proved that no permutation exists for which the sequence is good.

In the third test case, there are a total of 36 permutations for which the sequence is good. One of them is the permutation [1,5,4,2,3] which results in the sequence s=[0,0,3,2,0]. This is a good sequence because

·s1=s2&s3&s4&s5=0,s_1=s_2\&s_3\&s_4\&s_5=0,s1=s2&s3&s4&s5=0,
·s1&s2=s3&s4&s5=0,s_1\&s_2=s_3\&s_4\&s_5=0,s1&s2=s3&s4&s5=0,
·s1&s2&s3=s4&s5=0,s_1\&s_2\&s_3=s_4\&s_5=0,s1&s2&s3=s4&s5=0,
·s1&s2&s3&s4=s5=0.s_1\&s_2\&s_3\&s_4=s_5=0.s1&s2&s3&s4=s5=0.

问题链接：CodeForces - 1513B AND Sequences
问题简述：（略）
问题分析：（略）
AC的C++语言程序如下：

/* CodeForces - 1513B AND Sequences */#include <bits/stdc++.h>using namespace std;typedef long long LL;
const int MOD = 1e9 + 7;
const int N = 2e5;
int a[N];int main()
{int t, n, res;scanf("%d", &t);while (t--) {scanf("%d", &n);scanf("%d", &res);a[0] = res;for (int i = 1; i < n; i++) {scanf("%d", &a[i]);res &= a[i];}LL cnt = 0, ans = 0;for (int i = 0; i < n; i++)if (a[i] == res) cnt++;if (cnt >= 2) {ans = cnt * (cnt - 1) % MOD;for (int i = 1; i <= n - 2; i++)ans *= i, ans %= MOD;}printf("%lld\n", ans);}return 0;
}

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