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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

#[derive(Copy, Clone, Debug, Eq, PartialEq)]
pub struct ModInt(u32);

impl ModInt {
    pub const MOD: u32 = 1_000_000_007;

    pub fn inv(self) -> Self {
        if self.0 == 0 {
            panic!();
        }
        self.pow(Self::MOD - 2)
    }

    pub fn one() -> Self {
        Self(1)
    }

    pub fn pow(self, e: u32) -> Self {
        if e == 0 {
            return Self::new(1);
        }
        let mut res = self.pow(e >> 1);
        res *= res;
        if e & 1 == 1 {
            res *= self;
        }
        res
    }

    pub fn zero() -> Self {
        Self(0)
    }

    fn new(n: i64) -> Self {
        let mut n = n % (Self::MOD as i64);
        if n.is_negative() {
            n += Self::MOD as i64;
        }
        Self(n as u32)
    }
}

impl From<i32> for ModInt {
    fn from(n: i32) -> Self {
        ModInt::from(n as i64)
    }
}

impl From<i64> for ModInt {
    fn from(n: i64) -> Self {
        Self::new(n)
    }
}

impl From<isize> for ModInt {
    fn from(n: isize) -> Self {
        ModInt::from(n as i64)
    }
}

impl From<u32> for ModInt {
    fn from(n: u32) -> Self {
        ModInt::from(n as u64)
    }
}

impl From<u64> for ModInt {
    fn from(n: u64) -> Self {
        Self::new(n as i64)
    }
}

impl From<usize> for ModInt {
    fn from(n: usize) -> Self {
        ModInt::from(n as u64)
    }
}

impl Into<i32> for ModInt {
    fn into(self) -> i32 {
        self.0 as i32
    }
}

impl Into<i64> for ModInt {
    fn into(self) -> i64 {
        self.0 as i64
    }
}

impl Into<isize> for ModInt {
    fn into(self) -> isize {
        self.0 as isize
    }
}

impl Into<u32> for ModInt {
    fn into(self) -> u32 {
        self.0
    }
}

impl Into<u64> for ModInt {
    fn into(self) -> u64 {
        self.0 as u64
    }
}

impl Into<usize> for ModInt {
    fn into(self) -> usize {
        self.0 as usize
    }
}

impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::ops::Add for ModInt {
    type Output = Self;

    fn add(self, rhs: Self) -> Self {
        Self::new((self.0 + rhs.0) as i64)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl std::ops::Div for ModInt {
    type Output = Self;

    fn div(self, rhs: Self) -> Self {
        self * rhs.inv()
    }
}

impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = Self;

    fn mul(self, rhs: Self) -> Self {
        Self::new((self.0 as i64) * (rhs.0 as i64))
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = Self;

    fn sub(self, rhs: Self) -> Self {
        Self::new((self.0 as i64) - (rhs.0 as i64))
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

fn solve() {
    input! {
        n: usize,
        av: [u64; n]
    };

    let max_digit = 60;
    let mut one_counts = vec![0_u64; max_digit];
    let mut zero_counts = vec![0_u64; max_digit];
    for &a in &av {
        for d in 0..max_digit {
            if (a >> d) & 1 == 1 {
                one_counts[d] += 1;
            } else {
                zero_counts[d] += 1;
            };
        }
    }
    let mut res = ModInt::zero();
    for &a in &av {
        for d in 0..max_digit {
            if (a >> d) & 1 == 1 {
                res += ModInt::from(1_u64 << d) * ModInt::from(zero_counts[d]);
                one_counts[d] -= 1;
            } else {
                res += ModInt::from(1_u64 << d) * ModInt::from(one_counts[d]);
                zero_counts[d] -= 1;
            };
        }
    }
    println!("{}", res);
}

fn main() {
    std::thread::Builder::new()
        .name("big stack size".into())
        .stack_size(256 * 1024 * 1024)
        .spawn(|| {
            solve();
        })
        .unwrap()
        .join()
        .unwrap();
}