Problem:
Score : 600 points

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php

const MOD = 10 ** 9 + 7;

fscanf(STDIN, "%d%d%d%d", $r_1, $c_1, $r_2, $c_2);

$factorials = [1, 1];
$inv_factorials = [1, 1];
$inv_numbers = [null, 1];
for ($i = 2; $i <= $r_2 + $c_2 + 2; ++$i) {
    $factorials[$i] = $factorials[$i - 1] * $i % MOD;
    $inv_numbers[$i] = MOD - $inv_numbers[MOD % $i] * intdiv(MOD, $i) % MOD;
    $inv_factorials[$i] = $inv_factorials[$i - 1] * $inv_numbers[$i] % MOD;
}

echo frc($r_2 + 1, $c_2 + 1) - frc($r_1, $c_2 + 1) - frc($r_2 + 1, $c_1) + frc($r_1, $c_1);

function frc(int $r, int $c): int
{
    global $factorials;
    global $inv_factorials;

    return ($factorials[$r + $c] * $inv_factorials[$r]) % MOD * $inv_factorials[$c] % MOD;
}