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 Python (3.8.2) (judge verdict: Accepted)

import sys
from random import *
from collections import *
from heapq import *

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def MI1(): return map(int1, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
dij = [(1, 0), (-1, 0), (0, 1), (0, -1)]

# 内部で1-indexedに変えるので入力は0-indexedでよい
# i項目までの和（i含む）
class BitSum:
    def __init__(self, n):
        self.n = n+1
        self.table = [0]*self.n

    def add(self, i, x):
        i += 1
        while i < self.n:
            self.table[i] += x
            i += i & -i

    # [0,i]の和
    def sum(self, i):
        i += 1
        res = 0
        while i > 0:
            res += self.table[i]
            i -= i & -i
        return res

    # [l,r)の和
    def sumlr(self, l, r):
        if l == r: return 0
        if l == 0: return self.sum(r-1)
        return self.sum(r-1)-self.sum(l-1)

    # 数列を度数分布とみたときに、x番目がどのインデックスにあるかを返す
    # xが大きすぎるときは配列の長さnを返す
    def rank(self, x):
        idx = 0
        for lv in range((self.n-1).bit_length()-1, -1, -1):
            mid = idx+(1 << lv)
            if mid >= self.n: continue
            if self.table[mid] < x:
                x -= self.table[mid]
                idx += 1 << lv
        return idx

n,q=MI()
aa=LI()
bit=BitSum(n)
for i,a in enumerate(aa):bit.add(i,a)
for _ in range(q):
    t,a,b=MI()
    if t:print(bit.sumlr(a,b))
    else:bit.add(a,b)