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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<stdint.h>
#include<tgmath.h>
#include<stdbool.h>
#include<sys/queue.h>
#include<time.h>
#define ll long long
#define min(a, b) ((a) > (b) ? (b) : (a))
#define max(a, b) ((a) > (b) ? (a) : (b))

const ll mod = 1000000007;
ll modpow(ll x, ll y, ll m){
    if(y == 0ll)return 1ll;
    ll res = 1ll, tmp = x;
    while(y){
        if(y&1) res = res * tmp % m;
        tmp = tmp * tmp % m;
        y >>= 1;
    }
    return res;
}
ll pom(ll x, ll y){
    return modpow(x, y, mod);
}

ll n, a, b[99] = {}, ans = 0;

main(){
	scanf("%lld", &n);
	for(int i=0; i<n; i++){
		scanf("%lld", &a);
		for(int j=0; j<=60; j++){
			b[j] += (a>>j) & 1;
		}
	}
	for(int i=0; i<60; i++){
		ans += pom(2, i) * b[i] % mod * (n - b[i]) % mod;
		ans %= mod;
	}
	printf("%lld\n", ans);
	return 0;
}