Prefix Sum Queries

Given an array of n integers, your task is to process q queries of the following types:

update the value at position k to u

what is the maximum prefix sum in range [a,b]?

Empty prefixes (with sum 0) are allowed.

Input

The first input line has two integers n and q: the number of values and queries. The second line has n integers x_1,x_2,\dots,x_n: the array values. Finally, there are q lines describing the queries. Each line has three integers: either "1 k u" or "2 a b".

Output

Print the result of each query of type 2.

Constraints

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

$-10^9 \le x_i, u \le 10^9$

$1 \le k \le n$

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

Example

Input

8 4
1 2 -1 3 1 -5 1 4
2 2 6
1 4 -2
2 2 6
2 3 4

Output

5
2
0