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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defparameter const (+ 7 (expt 10 9)))
(defparameter r1 (read))
(defparameter c1 (read))
(defparameter r2 (read))
(defparameter c2 (read))

(defun fact (n)
  (if (= n 1)
      1
      (* n (fact (1- n)))))

(defun comb (r c)
  (/ (fact (+ r c)) (fact r) (fact c)))

(format t "~A" (loop with count = 0
                     for r from r1 to r2
                     do (loop for c from c1 to c2
                              do (incf count (mod (comb r c) 
                                                  const))
                                 (setf count (mod count const)))
                        (setf count (mod count const))
                     finally (return (mod count const))))