Problem:
RSQ and RAQ

Write a program which manipulates a sequence A = {a1, a2, . . . , an} with the following operations:

add(s, t, x): add x to as, as+1, ..., at.

getSum(s, t): report the sum of as, as+1, ..., at.

Note that the initial values of ai (i = 1, 2, . . . , n) are 0.

Input

n q
query1
query2
:
queryq

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query queryi is given in the following format:

0 s t x

or

1 s t

The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes getSum(s, t).

Output

For each getSum operation, print the sum;

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

1 ≤ s ≤ t ≤ n

0 ≤ x < 1000

Sample Input 1

3 5
0 1 2 1
0 2 3 2
0 3 3 3
1 1 2
1 2 3

Sample Output 1

4
8

Sample Input 2

4 3
1 1 4
0 1 4 1
1 1 4

Sample Output 2

0
4

Solution in Rust (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;
    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }
    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
}
#[allow(unused_macros)]
macro_rules ! get { ( $ t : ty ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . trim ( ) . parse ::<$ t > ( ) . unwrap ( ) } } ; ( $ ( $ t : ty ) ,* ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; let mut iter = line . split_whitespace ( ) ; ( $ ( iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) , ) * ) } } ; ( $ t : ty ; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ ( $ t : ty ) ,*; $ n : expr ) => { ( 0 ..$ n ) . map ( | _ | get ! ( $ ( $ t ) ,* ) ) . collect ::< Vec < _ >> ( ) } ; ( $ t : ty ;; ) => { { let mut line : String = String :: new ( ) ; stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; line . split_whitespace ( ) . map ( | t | t . parse ::<$ t > ( ) . unwrap ( ) ) . collect ::< Vec < _ >> ( ) } } ; }
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { println ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }

struct SEG {
    buf: Vec<(u64, u64)>,
    n: usize,
}

impl SEG {
    fn new(size: usize) -> SEG {
        let n = (1..).map(|i| 1 << i).find(|&x| x >= size).unwrap();

        SEG {
            buf: vec![(0, 0); 2 * n],
            n: n,
        }
    }

    fn add(&mut self, x: u64, a: usize, b: usize, k: usize, l: usize, r: usize) {
        self.eval(k, l, r);
        if r <= a || l >= b {
            return;
        }

        if a <= l && r <= b {
            self.buf[k].1 += (r - l) as u64 * x;
            // self.eval(k, l, r);
            return;
        }

        self.add(x, a, b, 2 * k + 1, l, (l + r) / 2);
        self.add(x, a, b, 2 * k + 2, (l + r) / 2, r);

        // self.buf[k].0 = self.buf[2 * k + 1].0 + self.buf[2 * k + 2].0;
        self.buf[k].0 = self.buf[2 * k + 1].0 + self.buf[2 * k + 1].1 + self.buf[2 * k + 2].0
            + self.buf[2 * k + 2].1;
    }

    fn eval(&mut self, k: usize, l: usize, r: usize) {
        if self.buf[k].1 > 0 {
            self.buf[k].0 += self.buf[k].1;

            if r - l > 1 {
                self.buf[2 * k + 1].1 += self.buf[k].1 / 2;
                self.buf[2 * k + 2].1 += self.buf[k].1 / 2;
            }
            self.buf[k].1 = 0;
        }
    }

    fn sum(&mut self, a: usize, b: usize, k: usize, l: usize, r: usize) -> u64 {
        if r <= a || l >= b {
            return 0;
        }

        if a <= l && r <= b {
            return self.buf[k].0 + self.buf[k].1;
        }

        self.eval(k, l, r);
        let vl = self.sum(a, b, 2 * k + 1, l, (l + r) / 2);
        let vr = self.sum(a, b, 2 * k + 2, (l + r) / 2, r);
        vl + vr
    }
}

fn main() {
    let (n, q) = get!(usize, usize);
    let mut seg = SEG::new(n);

    let n = seg.n;

    for _ in 0..q {
        let v = util::gets::<usize>();

        if v[0] == 0 {
            seg.add(v[3] as u64, v[1] - 1, v[2], 0, 0, n);
        } else {
            println!("{}", seg.sum(v[1] - 1, v[2], 0, 0, n));
        }
    }
}