A Fenwick Tree (also known as a Binary Indexed Tree) is a data structure on an array which enables fast ($O(\log n)$) updates and prefix sum queries on the underlying data.
For this problem, implement a Fenwick Tree to support operations of two types: (a) increment an element in the array or (b) query the prefix sum of a portion of the array.
The first line of input contains two integers $N$, $Q$, where $1 \le N \le 5\, 000\, 000$ is the length of the array and $0 \le Q \le 5\, 000\, 000$ is the number of operations. Then follow $Q$ lines giving the operations. There are two types of operations:
“+ $i$ $\delta $” indicates that $a[i]$ is incremented by $\delta $, where $0 \le i < N$ and $-10^9 \le \delta \le 10^9$ (both are integers)
“? $i$” is a query for the value of $a + a + \ldots + a[i-1]$, where $0 \le i \le N$ (for $i = 0$ this is interpreted as an empty sum)
You should assume that every array entry is initially $0$.
For each query in the input, output one line giving the answer to that query.
|Sample Input 1||Sample Output 1|
10 4 + 7 23 ? 8 + 3 17 ? 8
|Sample Input 2||Sample Output 2|
5 4 + 0 -43 + 4 1 ? 0 ? 5