Problem:
Range Sum Query

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

add(i, x): add x to ai.

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

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

Input

n q
com1 x1 y1
com2 x2 y2
...
comq xq yq

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes add(xi, yi) and '1' denotes getSum(xi, yi).

Output

For each getSum operation, print the sum in a line.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 1 ≤ xi ≤ n, 0 ≤ yi ≤ 1000.

If comi is 1, then 1 ≤ xi ≤ n, 1 ≤ yi ≤ n.

Sample Input 1

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

Sample Output 1

3
2

Solution in Python3 (judge verdict: Accepted)

import math


class SegmentTree:
    __slots__ = ["elem_size", "tree_size", "tree"]

    def __init__(self, a: list, default: int):
        real_size = len(a)
        self.elem_size = 1 << math.ceil(math.log2(real_size))
        self.tree_size = 2 * self.elem_size + 1
        self.tree = [default] * (self.elem_size - 1) + a + [default] * (self.elem_size - real_size)

    def get_range_index(self, x, y, k=0, l_end=0, r_end=None):
        '''[x, y], tree[k], [l_end, r_end)'''
        if r_end is None:
            r_end = self.elem_size

        if l_end == x and y == r_end-1:
            return [k]
        elif not l_end <= x <= y < r_end:
            return []

        mid = (l_end + r_end) // 2
        left_y = y if y < mid-1 else mid-1
        right_x = x if x > mid else mid

        left = self.get_range_index(x, left_y, 2*k+1, l_end, mid)
        right = self.get_range_index(right_x, y, 2*k+2, mid, r_end)
        return left + right

    def get_value(self, x, y):
        tree = self.tree
        index_list = self.get_range_index(x, y)

        return sum(tree[n] for n in index_list)

    def update_tree(self, k: int):
        tree = self.tree

        while k > 0:
            k = (k-1) // 2
            left, right = tree[2*k+1], tree[2*k+2]
            tree[k] = left + right

    def set_value(self, i: int, value: int, op: str):
        k = self.elem_size - 1 + i
        if op == "=":
            self.tree[k] = value
        elif op == "+":
            self.tree[k] += value
        self.update_tree(k)


n, q = map(int, input().split())
rsq = SegmentTree([0]*n, 0)
ans = []
for _ in [0]*q:
    c, x, y = map(int, input().split())
    if c == 0:
        rsq.set_value(x-1, y, "+")
    else:
        ans.append(rsq.get_value(x-1, y-1))
print("\n".join([str(n) for n in ans]))