Lazy propagation in Segment Tree

In the last last tutorial we learned how to build a Segment tree, query it and update point values to it. In this tutorial we will learn a useful technique Lazy Propagation for Segment trees. Using lazy propagation we can update a range in the tree efficiently. In this technique we update the value in a lazy manner, as the name suggests itself. Being lazy, values are not updated unless needed. Hence “lazy propagation” roughly translates to propagating values from root in a lazy manner.

Let’s make it clear with an example. Suppose we’ve built a Segment tree and there are two types of queries available on the tree. First one is update, which adds some value to nodes in a particular range. Second type is query for sum, which asks for sum of node values for a given range. In lazy propagation, “Lazy” refers to the idea that we will not update the range down to the leaf nodes every time it is called. Because the query for sum is called in the last, we will accumulate the values in an another array every time update() is called and these accumulated values will provide sum only for query which asks for sum in a range. Let’s take an example to make the concept clear.

Question
You are given an array of N elements, which are initially all 0. After that you will be given C commands. They are:
* 0 p q v — you have to add v to all numbers in the range of p to q (inclusive), where p and q are two indexes of the array.

* 1 p q — output a line containing a single integer which is the sum of all the array elements between p and q (inclusive)

Input:
In the first line you’ll be given T, number of test cases.

Each test case will start with N (N<=100 000) and C (C<=100 000). After that you’ll be given C commands in the format as mentioned above. 1 <= p,q <= N and 1 <= v <= 10⁷.

Output:
Print the answers of the queries.

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