Many Many Paths

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).

Examples

Input

1 1 2 2

Output

14

Input

314 159 2653 589

Output

602215194

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

r_1 c_1 r_2 c_2

outputFormat

Output

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

Examples

Input

1 1 2 2

Output

14

Input

314 159 2653 589

Output

602215194

样例

314 159 2653 589

602215194