#include<bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x...) do { cout << "\033[32;1m " << #x << " -> "; err(x); } while (0)
void err() { cout << "\033[39;0m" << endl; }
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x) { for (auto v: a) cout << v << ' '; err(x...); }
template<typename T, typename... A>
void err(T a, A... x) { cout << a << ' '; err(x...); }
#else
#define dbg(...)
#endif
typedef long long ll;
typedef pair<int,int> pi;
typedef vector<int> vi;
template<class T> using vc=vector<T>;
template<class T> using vvc=vc<vc<T>>;
template<class T> void mkuni(vector<T>&v)
{
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}
ll rand_int(ll l, ll r) //[l, r]
{
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class T>
void print(T x,int suc=1)
{
    cout<<x;
    if(suc==1) cout<<'\n';
    else cout<<' ';
}
template<class T>
void print(const vector<T>&v,int suc=1)
{
    for(int i=0;i<v.size();i++)
    print(v[i],i==(int)(v.size())-1?suc:2);
}
const int maxn = 5e5 + 5;
const int mod = 1e9 + 7;
int t, n, a[65];
ll x[maxn];
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> t;
    while (t--) {
        cin >> n;
        for (int i = 0; i < n; i++) {
            cin >> x[i];
            ll tmp = x[i], pos = 0;
            while (tmp) {
                if (tmp & 1) a[pos]++;
                tmp >>= 1;
                pos++;
            }
        }
        ll ans = 0;
        for (int i = 0; i < n; i++) {
            ll tmp = x[i], cc = 1, pos = 0, sum = 0, ssum = 0;
            for (int j = 0; j <= 60; j++) {
                if ((x[i] >> j) & 1)
                    sum = (sum + n * cc % mod) % mod;
                else
                    sum = (sum + a[j] * cc % mod) % mod;
                cc <<= 1;
                cc %= mod;
            }
            cc = 1, pos = 0;
            for (int j = 0; j <= 60; j++) {
                if ((x[i] >> j) & 1)
                    ssum = (ssum + a[j] * cc % mod) % mod;
                cc <<= 1;
                cc %= mod;
            }
            ans = (ans + sum * ssum % mod) % mod;
        }
        cout << ans << '\n';
        for (int i = 0; i < 62; i++)
            a[i] = 0;
    }
}
### Prompt

Your challenge is to write a Cpp solution to the following problem:

Only a few know that Pan and Apollo weren't only battling for the title of the GOAT musician. A few millenniums later, they also challenged each other in math (or rather in fast calculations). The task they got to solve is the following:

Let x_1, x_2, …, x_n be the sequence of n non-negative integers. Find this value: $$$∑_{i=1}^n ∑_{j=1}^n ∑_{k=1}^n (x_i   \&   x_j) ⋅ (x_j   |   x_k)$$$

Here \& denotes the [bitwise and,](https://en.wikipedia.org/wiki/Bitwise_operation#AND) and | denotes the [bitwise or.](https://en.wikipedia.org/wiki/Bitwise_operation#OR)

Pan and Apollo could solve this in a few seconds. Can you do it too? For convenience, find the answer modulo 10^9 + 7.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 1 000) denoting the number of test cases, then t test cases follow.

The first line of each test case consists of a single integer n (1 ≤ n ≤ 5 ⋅ 10^5), the length of the sequence. The second one contains n non-negative integers x_1, x_2, …, x_n (0 ≤ x_i < 2^{60}), elements of the sequence.

The sum of n over all test cases will not exceed 5 ⋅ 10^5.

Output

Print t lines. The i-th line should contain the answer to the i-th text case.

Example

Input


8
2
1 7
3
1 2 4
4
5 5 5 5
5
6 2 2 1 0
1
0
1
1
6
1 12 123 1234 12345 123456
5
536870912 536870911 1152921504606846975 1152921504606846974 1152921504606846973


Output


128
91
1600
505
0
1
502811676
264880351

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x...) do { cout << "\033[32;1m " << #x << " -> "; err(x); } while (0)
void err() { cout << "\033[39;0m" << endl; }
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x) { for (auto v: a) cout << v << ' '; err(x...); }
template<typename T, typename... A>
void err(T a, A... x) { cout << a << ' '; err(x...); }
#else
#define dbg(...)
#endif
typedef long long ll;
typedef pair<int,int> pi;
typedef vector<int> vi;
template<class T> using vc=vector<T>;
template<class T> using vvc=vc<vc<T>>;
template<class T> void mkuni(vector<T>&v)
{
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}
ll rand_int(ll l, ll r) //[l, r]
{
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class T>
void print(T x,int suc=1)
{
    cout<<x;
    if(suc==1) cout<<'\n';
    else cout<<' ';
}
template<class T>
void print(const vector<T>&v,int suc=1)
{
    for(int i=0;i<v.size();i++)
    print(v[i],i==(int)(v.size())-1?suc:2);
}
const int maxn = 5e5 + 5;
const int mod = 1e9 + 7;
int t, n, a[65];
ll x[maxn];
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> t;
    while (t--) {
        cin >> n;
        for (int i = 0; i < n; i++) {
            cin >> x[i];
            ll tmp = x[i], pos = 0;
            while (tmp) {
                if (tmp & 1) a[pos]++;
                tmp >>= 1;
                pos++;
            }
        }
        ll ans = 0;
        for (int i = 0; i < n; i++) {
            ll tmp = x[i], cc = 1, pos = 0, sum = 0, ssum = 0;
            for (int j = 0; j <= 60; j++) {
                if ((x[i] >> j) & 1)
                    sum = (sum + n * cc % mod) % mod;
                else
                    sum = (sum + a[j] * cc % mod) % mod;
                cc <<= 1;
                cc %= mod;
            }
            cc = 1, pos = 0;
            for (int j = 0; j <= 60; j++) {
                if ((x[i] >> j) & 1)
                    ssum = (ssum + a[j] * cc % mod) % mod;
                cc <<= 1;
                cc %= mod;
            }
            ans = (ans + sum * ssum % mod) % mod;
        }
        cout << ans << '\n';
        for (int i = 0; i < 62; i++)
            a[i] = 0;
    }
}
```