# Practice on Toph

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## Just Another Range Query

This is another simple range query problem where you will perform some updates and answer some queries. Let’s take an array **A** of length **N**. Initially, **A[i] = i** for each **i** in the range **[1,N]**.

You will have to perform **Q** operations on this array. There will be two types of operations:

**1 L R V**- which means that you will have to subtract**V**from all**A[i]**such that**L ≤ i ≤ R**.**2 L R**- which means that you will have to print the sum of all**A[i]**such that**L ≤ i ≤ R**.

### Input

In the first line of input, there will be two integers **N** and **Q (1 ≤ N ≤ 10 ^{9}, 1 ≤ Q ≤ 10^{5})** which are the length of the array and number of operations to perform respectively.

Next **Q** lines will contain the description of the operations to perform in the format **1 L R V** or **2 L R (1 ≤ L ≤ R ≤ N, 1 ≤ V ≤ 10 ^{5})**.

### Output

For each operation of the format **2 L R**, print the answer of the query in a single line.

### Samples

Input | Output |
---|---|

10 5 2 1 5 1 4 8 10 2 2 7 1 1 10 1 2 1 10 | 15 -13 -5 |

#### SMAN2901

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