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: Runtime Error)

def cmb(n,r,mod):
  if r<0 or r>n:
    return 0
  r=min(r,n-r)
  return g1[n]*g2[r]*g2[n-r]%mod
 
r1,c1,r2,c2=map(int,input().split())
mod=10**9+7

g1=[1,1]
g2=[1,1]
inverse=[0,1]
 
for i in range(2,10**6+1):
  g1.append((g1[-1]*i)%mod)
  inverse.append((-inverse[mod%i]*(mod//i))%mod)
  g2.append((g2[-1]*inverse[-1])%mod)

def g(r,c):
  ans=0
  for i in range(1,c+1):
    ans+=cmb(r+i-1,i,mod)
  return ans

print((g(r2+1,c2+1)-g(r2+1,c1)-g(r1,c2+1)+g(r1,c1)+mod)%mod)