Problem Statement

Snuke is standing on a two-dimensional plane. In one operation, he can move by $1$ in the positive $x$-direction, or move by $1$ in the positive $y$-direction.

Let us define a function $f(r, c)$ as follows:

• $f(r,c) :=$ (The number of paths from the point $(0, 0)$ to the point $(r, c)$ that Snuke can trace by repeating the operation above)

Given are integers $r_1$, $r_2$, $c_1$, and $c_2$. Find the sum of $f(i, j)$ over all pair of integers $(i, j)$ such that $r_1 ≤ i ≤ r_2$ and $c_1 ≤ j ≤ c_2$, and compute this value modulo $(10^9+7)$.

Constraints

• $1 ≤ r_1 ≤ r_2 ≤ 10^6$
• $1 ≤ c_1 ≤ c_2 ≤ 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

Output

Print the sum of $f(i, j)$ modulo $(10^9+7)$.