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)

class BIT:
    """
    Binary Index Tree
    ###1-origin####

    add :L[i]+=x
    sum: sum(L[:l])
    range_sum : sum(L[l:r])

    #material http://hos.ac/slides/20140319_bit.pdf
    """

    def __init__(self, N, init_val=0):
        self.init_val = init_val
        self.size = N
        self.L = [init_val]*(N+1)

    def sum(self, r):
        """
        sum[,r)
        calc sum from L[0] to L[r-1]
        """
        ret = self.init_val
        while r > 0:
            ret += self.L[r]
            r -= r & (-r)

        return ret

    def range_sum(self, l, r):
        
        """
        idx周りが怪しい?
        sum[l,r)
        calc sum from L[l] to L[r-1]
        """
        return self.sum(r-1)-self.sum(l-1)

    def add(self, i, x):
        """
        L[i] += x
        """
        while i <= self.size:
            self.L[i] += x
            i += i & (-i)

    def bisect(self,k:float)->int:
        """ binary search on BIT
        get index x s.t self.sum(,)>=k

        RETURN:
            res:index of x
        """
        k+=1 #convert k into 1-index

        res=0
        N=1
        while N<self.size:
            N*=2

        i=N//2
        while i>0:
            if(res+i<self.size and self.L[res+i]<k): #move to rignt on tree
                k-=self.L[res+i]
                res+=i
            #else move to left
            i//=2
        return res+1

N,Q = map(int,input().split())

B=BIT(N)
A=list(map(int,input().split()))
for i in range(N):
    B.add(i+1,A[i])

for _ in range(Q):
    v,l,r = map(int,input().split())
    if v==0:
        B.add(l+1,r)
    else:
        print(B.range_sum(l+1,r+1))