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 PyPy3 (7.3.0) (judge verdict: Accepted)

import math


class BinaryIndexedTree():
    def __init__(self, N):
        self.N = N
        self.arr = [0] * (N+1)

    def query(self, i):
        ret = 0
        i += 1
        while i:
            ret += self.arr[i]
            lsb = i & (-i)
            i -= lsb
        return ret

    def add(self, i, v):
        i += 1
        while i < self.N+1:
            lsb = i & (-i)
            self.arr[i] += v
            i += lsb

    def search(self, x):
        pos = 0
        cur = 0
        idx = 2 ** int(math.log(self.N, 2))
        while idx >= 1:
            if pos + idx <= self.N and cur + self.arr[pos+idx] < x:
                cur += self.arr[pos+idx]
                pos += idx
            idx //= 2
        return pos


def main():
    N, Q = map(int, input().split())
    A = list(map(int, input().split()))
    bit = BinaryIndexedTree(N)
    for i, a in enumerate(A):
        bit.add(i, a)
    for _ in range(Q):
        qtype, a, b = map(int, input().split())
        if qtype == 0:
            bit.add(a, b)
        else:
            ans = bit.query(b-1) - bit.query(a-1)
            print(ans)


if __name__ == "__main__":
    main()