output_description: Print the answer.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      S
attempt: mod = 10**9 + 7
  
  
  class Solution:
      def FactorialMod(self, n):
          if n <= 1:
              return 1
          else:
              return n * self.FactorialMod(n - 1) % mod
  
      def ModInv(self, p):
          if p <= 1:
              return 1
          return (-self.ModInv(mod % p) * (mod // p)) % mod
  
      def FactorialModInv(self, p):
          if p <= 1:
              return 1
          return modinv_table[p] * self.FactorialModInv(p - 1)
  
      def Solve(self, n):
          ans = 0
          # Fill in the modinv_table
          for p in range(2, n + 1):
              modinv_table[p] = (-modinv_table[mod % p] * (mod // p)) % mod
          # print(modinv_table)
          for item in range(1, max_items + 1):
              print("----------------------------------")
              print("item", item)
              max_value = S - 3 * item
              print("max_value", max_value)
              add = self.CalculateAddition(max_value, item)
              print("add", add)
              ans += add
              ans %= mod
          return ans
  
      def CalculateAddition(self, max_value, item):
          if max_value == 0:
              return 1
          add = 1
          add = add * self.FactorialMod(max_value + item - 1) % mod
          add = add * self.FactorialModInv(max_value) % mod
          add = add * self.FactorialModInv(item - 1) % mod
          return add
  
  
  S = int(input())
  if S <= 2:
      print(0)
      exit()
  
  max_items = S // 3
  # print("max_items", max_items)
  modinv_table = [-1] * (S + 1)
  modinv_table[1] = 1
  
  sol = Solution()
  print(sol.Solve(S))
  
problem_description: Statement
  
  Given is an integer S. Find how many sequences there are whose terms are all
  integers greater than or equal to 3, and whose sum is equal to S. The answer
  can be very large, so output it modulo 10^9 + 7.
samples: [{"input": "7", "output": "3\n    \n\n3 sequences satisfy the condition: \\\\{3,4\\\\}, \\\\{4,3\\\\} and \\\\{7\\\\}.\n\n* * *"}, {"input": "2", "output": "0\n    \n\nThere are no sequences that satisfy the condition.\n\n* * *"}, {"input": "1729", "output": "294867501"}]