**Time limit:**1.00 s**Memory limit:**512 MB

- Increase the first value in range $[a,b]$ by $1$, the second value by $2$, the third value by $3$, and so on.

- Calculate the sum of values in range $[a,b]$.

**Input**

The first input line has two integers $n$ and $q$: the size of the array and the number of queries.

The next line has $n$ values $t_1,t_2,\dots,t_n$: the initial contents of the array.

Finally, there are $q$ lines describing the queries. The format of each line is either "1 $a$ $b$" or "2 $a$ $b$".

**Output**

Print the answer to each sum query.

**Constraints**

- $1 \le n, q \le 2 \cdot 10^5$

- $1 \le t_i \le 10^6$

- $1 \le a \le b \le n$

**Example**

Input:

`5 3`

4 2 3 1 7

2 1 5

1 1 5

2 1 5

Output:

`17`

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