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: Accepted)

r1,c1,r2,c2=map(int,input().split())
MOD=10**9+7
idx=r2+c2+2
perm=[1]*(idx+1)
perm_inv=[1]*(idx+1)
for i in range(1,idx+1):
    perm[i]=perm[i-1]*i
    perm[i]%=MOD
def inv_mod(a):
  return pow(a,MOD-2,MOD)
perm_inv[-1]=inv_mod(perm[-1])
for i in range(idx-1,-1,-1):
    perm_inv[i]=perm_inv[i+1]*(i+1)
    perm_inv[i]%=MOD
def comb(i,j):
    buf=perm[i+j+2]
    buf*=perm_inv[i+1]
    buf%=MOD
    buf*=perm_inv[j+1]
    buf%=MOD
    return buf
res=comb(r2,c2)
res-=comb(r2,c1-1)
res-=comb(r1-1,c2)
res+=comb(r1-1,c1-1)
print(res%MOD)