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(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::str::FromStr;
use std::io::*;
use std::collections::*;
use std::cmp::*;

struct Scanner<I: Iterator<Item = char>> {
    iter: std::iter::Peekable<I>,
}

macro_rules! exit {
    () => {{
        exit!(0)
    }};
    ($code:expr) => {{
        if cfg!(local) {
            writeln!(std::io::stderr(), "===== Terminated =====")
                .expect("failed printing to stderr");
        }
        std::process::exit($code);
    }}
}

impl<I: Iterator<Item = char>> Scanner<I> {
    pub fn new(iter: I) -> Scanner<I> {
        Scanner {
            iter: iter.peekable(),
        }
    }

    pub fn safe_get_token(&mut self) -> Option<String> {
        let token = self.iter
            .by_ref()
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        if token.is_empty() {
            None
        } else {
            Some(token)
        }
    }

    pub fn token(&mut self) -> String {
        self.safe_get_token().unwrap_or_else(|| exit!())
    }

    pub fn get<T: FromStr>(&mut self) -> T {
        self.token().parse::<T>().unwrap_or_else(|_| exit!())
    }

    pub fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.get()).collect()
    }

    pub fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }

    pub fn char(&mut self) -> char {
        self.iter.next().unwrap_or_else(|| exit!())
    }

    pub fn chars(&mut self) -> Vec<char> {
        self.get::<String>().chars().collect()
    }

    pub fn mat_chars(&mut self, row: usize) -> Vec<Vec<char>> {
        (0..row).map(|_| self.chars()).collect()
    }

    pub fn line(&mut self) -> String {
        if self.peek().is_some() {
            self.iter
                .by_ref()
                .take_while(|&c| !(c == '\n' || c == '\r'))
                .collect::<String>()
        } else {
            exit!();
        }
    }

    pub fn peek(&mut self) -> Option<&char> {
        self.iter.peek()
    }
}

struct BinaryIndexedTree<T> {
    n: usize,
    bit: Vec<Vec<T>>,
}

use std::ops::{Add, Sub, Mul, Neg, AddAssign};

impl<T> BinaryIndexedTree<T>
where T: Copy
       + Default
       + Add<Output=T>
       + Sub<Output=T>
       + Mul<Output=T>
       + Neg<Output=T>
       + AddAssign
       + From<u32>
{
    fn new(n: usize) -> Self {
        BinaryIndexedTree {
            n: n + 1,
            bit: vec![vec![T::default(); n + 1]; 2],
        }
    }

    fn add(&mut self, l: usize, r: usize, v: T) {
        self.add_sub(0, l, -v * T::from(l as u32 - 1 as u32));
        self.add_sub(0, r, v * T::from(r as u32));
        self.add_sub(1, l, v);
        self.add_sub(1, r, -v);
    }

    fn add_sub(&mut self, p: usize, i: usize, v: T) {
        let mut idx = i;
        while idx < self.n {
            self.bit[p][idx] += v;
            idx += idx & (!idx+1);
        }
    }

    fn sum(&self, i: usize) -> T {
        self.sum_sub(0, i) + self.sum_sub(1, i) * T::from(i as u32)
    }

    fn sum_sub(&self, p: usize, i: usize) -> T {
        let mut ret = T::default();
        let mut idx = i;
        while idx > 0 {
            ret += self.bit[p][idx];
            idx -= idx & (!idx+1);
        }
        ret
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin.bytes().map(|c| c.unwrap() as char));
    let n: usize = sc.get();
    let q: usize = sc.get();
    let mut bit = BinaryIndexedTree::new(n);
    for _ in 0..q {
        let ty: usize = sc.get();
        let s: usize = sc.get();
        let t: usize = sc.get();
        if ty == 0 {
            let x: i64 = sc.get();
            bit.add(s, t, x);
        } else {
            let ans = bit.sum(t) - bit.sum(s - 1);
            println!("{}", ans);
        }
    }
}