input: from typing import List
  
  def count_stable_binary_arrays(z: int, o: int, l: int) -> int:
      """
      Given 3 positive integers z, o, and l, representing zeroes, ones, and a limit, respectively.
  
      A binary array arr is termed stable if:
  
      The count of 0s in arr equals z.
      The count of 1s in arr equals o.
      Any subarray of arr with a length greater than l must include both 0 and 1.
      Return the total count of such stable binary arrays.
  
      As the result might be very large, return it modulo 10^9 + 7.
  
      Examples:
      >>> z = 1, o = 1, l = 2
      2
      >>> z = 1, o = 2, l = 1
      1
      >>> z = 3, o = 3, l = 2
      14
  
      Constraints:
      1 <= z, o, l <= 200
      """
output:     
      MOD = 10**9 + 7
  
      # dp[k][i][j] will store the number of stable binary arrays of length k
      # with exactly i zeros and j ones.
      dp = [[[-1 for _ in range(o + 1)] for _ in range(z + 1)] for _ in range(z + o + 1)]
  
      def count(z, o, l, i, j, k):
          if i < 0 or j < 0:
              return 0
          if i == 0 and j == 0:
              return 1 if k <= l else 0
          if dp[k][i][j] != -1:
              return dp[k][i][j]
          
          # Place a 0 if possible
          place_zero = count(z, o, l, i - 1, j, k + 1)
          # Place a 1 if possible
          place_one = count(z, o, l, i, j - 1, k + 1)
          
          # Add both possibilities and store modulo MOD
          dp[k][i][j] = (place_zero + place_one) % MOD
          return dp[k][i][j]
  
      return count(z, o, l, z, o, 0)
  