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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

PRIME = 10 ** 9 + 7

r1, c1, r2, c2 = map(int, input().split())
maximum = r2 + c2

fac = [1 for i in range(maximum + 1)]
finv = [1 for i in range(maximum + 1)]
inv = [1 for i in range(maximum + 1)]

for i in range(2, maximum + 1):
    fac[i] = fac[i - 1] * i % PRIME
    inv[i] = PRIME - inv[PRIME % i] * (PRIME // i) % PRIME
    finv[i] = finv[i - 1] * inv[i] % PRIME

ans = 0
for x in range(r1, r2 + 1):
  for y in range(c1, c2 + 1):
    ans = (ans + fac[x + y] * (finv[x] * finv[y] % PRIME) % PRIME) % PRIME

print(ans)