Problem:
Score : 400 points

Problem Statement

We have N integers. The i-th integer is A_i.

Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

2 \leq N \leq 3 \times 10^5

0 \leq A_i < 2^{60}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the value \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

We have (1\mbox{ XOR } 2)+(1\mbox{ XOR } 3)+(2\mbox{ XOR } 3)=3+2+1=6.

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

Print the sum modulo (10^9+7).

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

#include <bits/stdc++.h>
using namespace std;
using namespace std::literals;
using Int = long long;
using Double = long double;
#define rep(i, n) for (int i = 0, i##_len = (int)(n); i < i##_len; i++)
#define reps(i, n) for (int i = 1, i##_len = (int)(n); i <= i##_len; i++)
#define ALL(v) (v).begin(), (v).end()
#define SZ(x) ((int)(x).size())
#define LEN(x) ((int)(x).length())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define PUTS(x) cout << (x) << endl;
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define F first
#define S second
#define perm(c)   \
    sort(ALL(c)); \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define IntsIn(v, n)                                 \
    auto v = vector<Int>(0);                         \
    for (int v##_i = 0; v##_i < (int)(n); v##_i++) { \
        Int v##_a;                                   \
        cin >> v##_a;                                \
        v.push_back(v##_a);                          \
    }
void setPrecision(int num = 20) {
    std::cout << std::fixed << std::setprecision(num);
}
template <typename T>
T Max(T a) {
    return a;
}
template <typename T, typename... Args>
T Max(T a, Args... args) {
    return std::max(Max(args...), a);
}
template <typename T>
T Min(T a) {
    return a;
}
template <typename T, typename... Args>
T Min(T a, Args... args) {
    return std::min(Min(args...), a);
}
template <typename T>
bool vector_contains(std::vector<T> vec, T value) {
    return (std::distance(vec.begin(), std::find(vec.begin(), vec.end(), value)) != vec.size());
}
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
    std::fill((T *)array, (T *)(array + N), val);
}
template <typename... Args>
std::string format(const std::string &fmt, Args... args) {
    size_t len = std::snprintf(nullptr, 0, fmt.c_str(), args...);
    std::vector<char> buf(len + 1);
    std::snprintf(&buf[0], len + 1, fmt.c_str(), args...);
    return std::string(&buf[0], &buf[0] + len);
}
string toStringWithBase(Int value, int base) {
    auto r = value % base;
    auto q = value / base;
    auto s = (r < 10) ? ('0' + r) : ('A' + (r - 10));
    if (q == 0) {
        return format("%c", s);
    } else {
        return format("%s%c", toStringWithBase(q, base).c_str(), s);
    }
}
string toStringWithBase(Int value, int base, int padding) {
    auto result = toStringWithBase(value, base);
    auto n = result.size();
    auto Result = ""s;
    for (int i = n + 1; i <= padding; i++) {
        Result += "0"s;
    }
    return Result + result;
}
const auto MOD = 1000000007LL;
int main() {
    Int n;
    cin >> n;
    IntsIn(v, n);
    auto counts = vector<Int>(64, 0);
    rep(i, 63) {
        for (auto a : v) {
            if ((((1LL << i) & a) >> i) == 1) counts[i]++;
        }
    }
    Int ans = 0;
    rep(i, 63) {
        auto x = (counts[i] % MOD) * ((n - counts[i]) % MOD) % MOD;
        rep(j, i) {
            x *= 2;
            x %= MOD;
        }
        ans += x;
        ans %= MOD;
    }
    PUTS(ans);
}