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 Python (3.4.3) (judge verdict: Runtime Error)

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

mod = 1000000007

# return an integer k s.t. (a * k) % p = 1 and 0 <= k < p.
def inversion(a):
    b = mod
    u, v = 1, 0
    while b >= 1:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u %= mod
    if u < 0:
        u += mod
    return u

fact = [0 for i in range(20003)]
for i in range(20003):
    if i <= 1:
        fact[i] = 1
    else:
        fact[i] = (fact[i-1] * i) % mod

# return nCr % p.
def combination(n, r):
    return (((fact[n] * inversion(fact[r])) % mod) * inversion(fact[n-r])) % mod

answer = (
combination(r2 + c2 + 2, r2 + 1) -
combination(r2 + c1 + 1, r2 + 1) -
combination(r1 + c2 + 1, c2 + 1) +
combination(r1 + c1    , c1    ) )

answer %= mod

if answer < 0:
    answer += mod

print(answer)