Problem:
Score : 100 points

Problem Statement

You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

0 p x: a_p \gets a_p + x

1 l r: Print \sum_{i = l}^{r - 1}{a_i}.

Constraints

1 \leq N, Q \leq 500,000

0 \leq a_i, x \leq 10^9

0 \leq p < N

0 \leq l_i < r_i \leq N

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N Q
a_0 a_1 ... a_{N - 1}
\textrm{Query}_0
\textrm{Query}_1
:
\textrm{Query}_{Q - 1}

Output

For each query of the latter type, print the answer.

Sample Input 1

5 5
1 2 3 4 5
1 0 5
1 2 4
0 3 10
1 0 5
1 0 3

Sample Output 1

15
7
25
6

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};
fn main() {
    input! {//
        n:usize,q:usize,
        a:[usize;n],
        qs:[(usize,usize,usize);q],
    }

    let mut bt = FenwickTree::new(MX, 0);
    for (i, &x) in a.iter().enumerate() {
        bt.add(i, x);
    }
    for &(x, l, r) in qs.iter() {
        match x {
            0 => {
                bt.add(l, r);
            }
            _ => {
                println!("{}", bt.sum(l, r));
            }
        }
    }
}
const MX: usize = 1010101;

pub struct FenwickTree<T> {
    n: usize,
    ary: Vec<T>,
    e: T,
}
impl<T: Clone + std::ops::AddAssign<T>> FenwickTree<T> {
    pub fn new(n: usize, e: T) -> Self {
        FenwickTree {
            n,
            ary: vec![e.clone(); n],
            e,
        }
    }
    pub fn accum(&self, mut idx: usize) -> T {
        let mut sum = self.e.clone();
        while idx > 0 {
            sum += self.ary[idx - 1].clone();
            idx &= idx - 1;
        }
        sum
    }
    /// performs data[idx] += val;
    pub fn add<U: Clone>(&mut self, mut idx: usize, val: U)
    where
        T: std::ops::AddAssign<U>,
    {
        let n = self.n;
        idx += 1;
        while idx <= n {
            self.ary[idx - 1] += val.clone();
            idx += idx & idx.wrapping_neg();
        }
    }
    /// Returns data[l] + ... + data[r - 1].
    pub fn sum(&self, l: usize, r: usize) -> T
    where
        T: std::ops::Sub<Output = T>,
    {
        self.accum(r) - self.accum(l)
    }
}