**Time limit:**1.50 s**Memory limit:**256 MB

Your task is to calculate answers for $q$ queries where the sum of numbers in an rectangular region in the grid is requested (modulo $10^9+7$). For example, in the following grid $n=2$ and the sum of numbers in the gray region is $74$:

**Input**

The first input line contains two integers $n$ and $q$: the size of the grid and the number of queries.

After this, there are $q$ lines, each containing four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-n \le x_1\le x_2 \le n$, $-n \le y_1 \le y_2 \le n$). This means that you should calculate the sum of numbers in a rectangular region with corners $(x_1, y_1)$ and $(x_2, y_2)$.

**Output**

You should output the answer for each query (modulo $10^9+7$).

**Example**

Input:

`2 3`

0 -2 1 1

-1 0 1 0

1 2 1 2

Output:

`74`

9

14

**Subtasks**

In all subtasks $1 \le q \le 100$.

**Subtask 1 (12 points)**

- $1 \le n \le 1000$

**Subtask 2 (15 points)**

- $1 \le n \le 10^9$

- $x_1=x_2$ and $y_1=y_2$

**Subtask 3 (17 points)**

- $1 \le n \le 10^5$

**Subtask 4 (31 points)**

- $1 \le n \le 10^9$

- $x_1=y_1=1$

**Subtask 5 (25 points)**

- $1 \le n \le 10^9$