Score : 600 points
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:
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).
Input is given from Standard Input in the following format:
r_1 c_1 r_2 c_2
Print the sum of f(i, j) modulo (10^9+7).
1 1 2 2
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.
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