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 (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp;
use std::io::Write;

// Input macro from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
  (source = $s:expr, $($r:tt)*) => {
    let mut iter = $s.split_whitespace();
    input_inner!{iter, $($r)*}
  };
  ($($r:tt)*) => {
    let s = {
      use std::io::Read;
      let mut s = String::new();
      std::io::stdin().read_to_string(&mut s).unwrap();
      s
    };
    let mut iter = s.split_whitespace();
    input_inner!{iter, $($r)*}
  };
}

macro_rules! input_inner {
  ($iter:expr) => {};
  ($iter:expr, ) => {};

  ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
    let $var = read_value!($iter, $t);
    input_inner!{$iter $($r)*}
  };
}

macro_rules! read_value {
  ($iter:expr, ( $($t:tt),* )) => {
    ( $(read_value!($iter, $t)),* )
  };

  ($iter:expr, [ $t:tt ; $len:expr ]) => {
    (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
  };

  ($iter:expr, chars) => {
    read_value!($iter, String).chars().collect::<Vec<char>>()
  };

  ($iter:expr, usize1) => {
    read_value!($iter, usize) - 1
  };

  ($iter:expr, [ $t:tt ]) => {{
    let len = read_value!($iter, usize);
    (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
  }};

  ($iter:expr, $t:ty) => {
    $iter.next().unwrap().parse::<$t>().expect("Parse error")
  };
}

const MOD: i64 = 1_000_000_007;

#[derive(Copy, Clone, Hash, Debug)]
struct ModInt {
  x: i64
}
impl ModInt {
  fn new(x: i64) -> Self {
    ModInt {
      x: x % MOD
    }
  }
  fn pow(self, e: i64) -> Self {
    if e == 0 {
      Self::new(1)
    } else if e % 2 == 1 {
      self.pow(e - 1) * self
    } else {
      let y = self.pow(e / 2);
      y * y
    }
  }
  #[allow(dead_code)]
  fn inv(self) -> Self {
    self.pow(MOD - 2)
  }
}
impl<T: Into<ModInt>> std::ops::Add<T> for ModInt {
  type Output = Self;
  fn add(self, other: T) -> Self {
    let other = other.into();
    let sum = self.x + other.x;
    ModInt {
      x: if sum >= MOD { sum - MOD } else { sum }
    }
  }
}
impl<T: Into<ModInt>> std::ops::Sub<T> for ModInt {
  type Output = Self;
  fn sub(self, other: T) -> Self {
    let other = other.into();
    let sum = self.x - other.x;
    ModInt {
      x: if sum < 0 { sum + MOD } else { sum }
    }
  }
}
impl<T: Into<ModInt>> std::ops::Mul<T> for ModInt {
  type Output = Self;
  fn mul(self, other: T) -> Self {
    let other = other.into();
    ModInt {
      x: self.x * other.x % MOD
    }
  }
}
impl<T: Into<ModInt>> std::ops::Div<T> for ModInt {
  type Output = Self;
  fn div(self, other: T) -> Self {
    let other = other.into();
    self * other.inv()
  }
}
impl From<i64> for ModInt {
  fn from(x: i64) -> Self {
    ModInt::new(x)
  }
}
impl std::fmt::Display for ModInt {
  fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
    self.x.fmt(f)
  }
}
impl<T: Into<ModInt>> std::ops::AddAssign<T> for ModInt {
  fn add_assign(&mut self, other: T) {
    *self = *self + other;
  }
}
impl<T: Into<ModInt>> std::ops::SubAssign<T> for ModInt {
  fn sub_assign(&mut self, other: T) {
    *self = *self - other;
  }
}
impl<T: Into<ModInt>> std::ops::MulAssign<T> for ModInt {
  fn mul_assign(&mut self, other: T) {
    *self = *self * other;
  }
}
impl<T: Into<ModInt>> std::ops::DivAssign<T> for ModInt {
  fn div_assign(&mut self, other: T) {
    *self = *self / other;
  }
}

fn main() {
  let out = std::io::stdout();
  let mut out = std::io::BufWriter::new(out.lock());
  macro_rules! puts {
    ($($format:tt)*) => (write!(out,$($format)*).unwrap());
  }
  input! {
    n: usize,
    a: [i64; n],
  }
  let mut ones = vec![0; 60];
  let mut ans = ModInt::new(0);
  for (c, &x) in a.iter().enumerate() {
    for (i, d) in ones.iter_mut().enumerate() {
      if (x >> i) & 1 == 0 {
        ans += ModInt::new(1 << i as i64) * *d;
      } else {
        ans += ModInt::new(1 << i as i64) * (c as i64 - *d);
        *d += 1;
      }
    }
  }

  puts!("{}\n", ans);
}