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;
/// Typedef
typedef long long           ll;
typedef vector<int>         vi;
typedef pair<int,int>       pii;

#define pb                  push_back
#define ppb                 pop_back
#define MP                  make_pair
#define ff                  first
#define ss                  second
#define sf                  scanf
#define pf                  printf
#define SQR(x)              ((x)*(x))
#define loop(i, y)          for(int i=0; i<int(y); i++)
#define FOR(i, x, y)        for(int i=int(x); i<int(y); i++)
#define ROF(i, x, y)        for(int i=int(x); i>=int(y); i--)
#define all(c)              c.begin(), c.end()
#define sz(c)               int(c.size())
#define clr(x, y)           memset(x, y, sizeof(x))
#define si(x)               scanf("%d", &x)
#define sii(x, y)           scanf("%d %d", &x, &y)
#define siii(x, y, z)       scanf("%d %d %d", &x, &y, &z)
#define sl(x)               scanf("%lld", &x)
#define sll(x, y)           scanf("%lld %lld", &x, &y)
#define slll(x, y, z)       scanf("%lld %lld %lld", &x, &y, &z)

#ifdef VAMP
     #define debug(...) __f(#__VA_ARGS__, __VA_ARGS__)
    template < typename Arg1 >
    void __f(const char* name, Arg1&& arg1){
        cout << name << " = " << arg1 << std::endl;
    }
    template < typename Arg1, typename... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args){
        const char* comma = strchr(names+1, ',');
        cout.write(names, comma - names) << " = " << arg1 <<" | ";
        __f(comma+1, args...);
    }
#else
    #define debug(...)
#endif
///******************************************START******************************************

/// Constants
#define MAX                 62
#define MOD                 1000000007
#define eps                 1e-9
#define INF                 0x3f3f3f3f3f3f3f3f // 4,557,430,888,798,830,399
#define inf                 0x3f3f3f3f // 1,061,109,567
#define PI                  acos(-1.0)  // 3.1415926535897932
#define VT                  int

int cnt[2][MAX];

int main(){
    #ifdef VAMP
        clock_t tStart = clock();
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
    int n; si(n);
    ll res = 0;
    FOR(i, 0, n){
        ll x; sl(x);
        FOR(j, 0, MAX){
            ll now = (x>>j)&1;
            res += (1LL<<j) % MOD * cnt[!now][j] % MOD;
            res %= MOD;
            cnt[now][j]++;
        }
    }
    cout<<res<<endl;


    #ifdef VAMP
        fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC);
    #endif
    return 0;
}