Bobo has a rectangle $A$. The coordinates of the bottom-left corner of the rectangle are $(x_1, y_1)$, and the coordinates of the top-right corner are $(x_2, y_2)$. Let $R(i, j)$ be the rectangle with bottom-left corner $(0, 0)$ and top-right corner $(i, j)$, and let $\mathrm{Area}(i, j)$ be the area of the union of rectangle $A$ and rectangle $R(i, j)$.

Given $a$ and $b$, calculate $\sum_{i = 1}^a \sum_{j = 1}^b \mathrm{Area}(i, j)$ modulo $(10^9+7)$.

Input

The input file contains multiple test cases. Process until the end of the file.

Each test case consists of two lines. The first line contains two integers $a$ and $b$, and the second line contains four integers $x_1, x_2, y_1, y_2$.

• $1 \leq a, b, x_1, x_2, y_1, y_2 \leq 10^9$
• $x_1 < x_2$, $y_1 < y_2$
• The number of test cases does not exceed $10^4$.

Output

For each test case, output an integer representing the required value.

Examples

Input 1

1 1
2 3 2 3
10 10
1 5 1 5
1000000000 1000000000
1 1000000000 1 1000000000

Output 1

2
3725
2793