output_description: Print the sum of f(i, j) modulo (10^9+7).
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      r_1 c_1 r_2 c_2
attempt: class ModComb:
      def __init__(self, MAX, mod=10**9 + 7):
          fac = [1, 1]
          finv = [1, 1]
          inv = [0, 1]
          for i in range(2, MAX):
              fac.append(fac[i - 1] * i % mod)
              inv.append(mod - inv[mod % i] * (mod // i) % mod)
              finv.append(finv[i - 1] * inv[i] % mod)
          self.fac, self.finv, self.mod = fac, finv, mod
  
      def nCk(self, n, k):
          if n < k or n < 0 or k < 0:
              return 0
          fac, finv, mod = self.fac, self.finv, self.mod
          return fac[n] * (finv[k] * finv[n - k] % mod) % mod
  
  
  mod = 10**9 + 7
  
  r1, c1, r2, c2 = map(int, input().split())
  
  mc = ModComb(r2 + c2 + 10)
  
  
  def f(i, j):
      return mc.nCk(i + j, i)
  
  
  print((f(r2 + 1, c2 + 1) - f(r2 + 1, c1) - f(r1, c2 + 1) + f(r1, c1)) % mod)
  
problem_description: 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).
samples: [{"input": "1 1 2 2", "output": "14\n    \n\nFor example, there are two paths from the point (0, 0) to the point (1, 1):\n(0,0) \u2192 (0,1) \u2192 (1,1) and (0,0) \u2192 (1,0) \u2192 (1,1), so f(1,1)=2.\n\nSimilarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.\n\n* * *"}, {"input": "314 159 2653 589", "output": "602215194"}]