Students at Idua High School are practicing the moving mass game in preparation for next year's sports festival. In this mass game, the students move and turn their bodies in accordance with the teacher's commands.
In the moving mass game, the teacher gives instructions to the students in the compartments numbered from $1$ to $N$. The compartments are lined up in a row from west to east, starting from 1. Initially, each student is in one of the compartments, all standing facing north. Each compartment is large enough to hold all the students. The teacher tells the students who are in which compartment at the time of instruction and how much they will move.
When the teacher shouts out the three numbers $a,b,c$, all the students in the compartments from $a$th to $b$th at that point move in a simultaneous manner according to the value of $c$, and also change their body orientation 180 degrees. If $c$ is a positive integer, the student moves east, if negative, the student moves west, and so on for one compartment per number size, and students who were facing north before the move will face south after the move, and students who were facing south will face north. In this case, students who are instructed to move to a compartment numbered less than $a$th will move to the $a$th compartment, and students who are instructed to move to a compartment numbered greater than $b$th will move to the $b$th compartment. This means that some students may not move at all, even if they are in the $a$th through $b$th compartments, but even these students will always change their body orientation 180 degrees.
The teacher giving the instructions believes that the orientation of the students at a given point in time has something to do with the beauty of the moving mass game. Therefore, he wants to know the number of students facing north minus the number of students facing south in the specified range of compartments immediately after the instruction at some point.
Given the number of compartments, the number of students, the number of the first compartment each student is in, and the information about the query to find the difference between the teacher's call and the number of students, for each query, write a program to find the number of students in the specified range of compartments facing north minus the number of students facing south.
The input is given in the following format.
$N$ $M$ $x_1$ $x_2$ : $x_M$ $Q$ $info_1$ $info_2$ : $info_Q$
The first line gives the number of compartments $N$ ($2 \leq N \leq 10^9=10$ to the $9$ power) and the number of students $M$ ($1 \leq M \leq 100,000$). In the next $M$ line, the number $x_i$ ($1 \leq x_i \leq N$) of the first compartment where the $i$th student is located is given. The next line is given the number $Q$ ($1 \leq Q \leq 100,000$) of information about the order and query. The subsequent $Q$ line gives the information $info_i$ about the order and query. The information is arranged in chronological order. Each $info_i$ is given in one of the following formats.
1 $a$ $b$ $c$
or
2 $d$ $e$
1 $a$ $b$ $c$ denotes the order that the students in the $a$th to $b$th compartments should change the direction they are facing while moving according to the number $c$. However, $1 \leq a \leq b \leq N$, $-N < c < N$ with $c\ne0$. 2 $d$ $e$ represents a query that reports the number of students facing north minus the number of students facing south for the students in the $d$th through $e$th compartments at that time. However, $1 \leq d \leq e \leq N$. More than one piece of information about the query can be given.
For each query, output on a single line the number of students facing north minus the number of students facing south in the compartment in the range specified by the query.
6 6 1 1 2 3 5 6 11 2 1 6 1 4 6 -2 2 2 4 2 3 4 1 1 4 1 2 1 1 2 2 2 2 3 3 2 4 4 2 5 5 2 6 6
6 0 -1 0 -2 -1 1 0 0