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 Ruby (2.3.3) (judge verdict: Runtime Error)

$memo = {}

def f(r, c)
  return $memo[r][c] if $memo.key?(r) && $memo[r].key?(c)
  return $memo[c][r] if $memo.key?(c) && $memo[c].key?(r)
  $memo[r] = {} unless $memo.key?(r)
  return $memo[r][c] = 0 if r == 0 && c == 0
  return $memo[r][c] = 1 if r == 0 || c == 0
  $memo[r][c] = (f(r - 1, c) + f(r, c - 1)) % 1000000007
end



$memo2 = {}
def g(r, c)
  return $memo2[r][c] if $memo2.key?(r) && $memo2[r].key?(c)
  return $memo2[c][r] if $memo2.key?(c) && $memo2[c].key?(r)
  $memo2[r] = {} unless $memo2.key?(r)
  return $memo2[r][c] = 0 if r == 0 && c == 0
  return $memo2[r][c] = r + c if r == 0 || c == 0
  $memo2[r][c] = (g(r - 1, c) + g(r, c - 1) + f(r, c) - g(r - 1, c - 1)) % 1000000007
end

r1, c1, r2, c2 = *gets.chomp.split.map(&:to_i)
puts g(r2, c2) - g(r2, c1 - 1) - g(r1 - 1, c2) + g(r1 - 1, c1 - 1)