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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program many_paths
    implicit none
    integer(8) r1, r2, c1, c2, i, k
    integer(8) :: ans1 = 1, ans2 = 1, ans3 = 1, ans4 = 1, ans = 0
    read *, r1, c1, r2, c2
    do i = r1+1, r1+c1
        ans1 = ans1 * i
        do k = i-r1, i-r1
            ans1 = ans1 / k
            if(k .eq. c1)exit
        end do
        if(i .eq. r1+c1)exit
    end do
    do i = r1+1, r1+c2
        ans2 = ans2 * i
        do k = i-r1, i-r1
            ans2 = ans2 / k
            if(k .eq. c2)exit
        end do
        if(i .eq. r1+c2)exit
    end do
    do i = r2+1, r2+c1
        ans3 = ans3 * i
        do k = i-r2, i-r2
            ans3 = ans3 / k
            if(k .eq. c1)exit
        end do
        if(i .eq. r2+c1)exit
    end do
    do i = r2+1, r2+c2
        ans4 = ans4 * i
        do k = i-r2, i-r2
            ans4 = ans4 / k
            if(k .eq. c2)exit
        end do
        if(i .eq. r2+c2)exit
    end do
    ans = mod(ans1+ans2+ans3+ans4, 10**9+7)
    print *, ans
end program