There is a sequence $a$ of length $n$. We use $a_i$ to denote the $i$-th element in this sequence. You should do the following three types of operations to this sequence.
$0\ x\ y\ t$: For every $x \le i \le y$, we use $min(a_i, t)$ to replace the original $a_i$'s value.
$1\ x\ y$: Print the maximum value of $a_i$ that $x \le i \le y$.
$2\ x\ y$: Print the sum of $a_i$ that $x \le i \le y$.
The first line of the input is a single integer $T$, indicating the number of testcases.
The first line contains two integers $n$ and $m$ denoting the length of the sequence and the number of operations.
The second line contains $n$ separated integers $a_1, \ldots, a_n$ ($\forall 1 \le i \le n, 0 \le a_i < 2^{31}$).
Each of the following $m$ lines represents one operation ($1 \le x \le y \le n, 0\le t < 2^{31}$).
It is guaranteed that $T=100$, $\sum n \le 1000000, \ \sum m \le 1000000$.
For every operation of type $1$ or $2$, print one line containing the answer to the corresponding query.