input: from typing import List
  from itertools import accumulate
  
  def find_house_paths(n: int, x: int, y: int) -> List[int]:
      """
      Given three integers n, x, and y, determine the city paths.
  
      There are houses numbered from 1 to n, linked by streets. A standard street joins house i and house i+1 for all 1 <= i <= n - 1. Additionally, there is a street between house x and house y.
  
      For every k where 1 <= k <= n, calculate how many pairs of houses (house1, house2) exist such that the least number of streets to travel from house1 to house2 is k.
  
      Return a 1-based list where the k-th element represents the count of house pairs needing at least k streets for the shortest path.
  
      Note: x and y may be identical.
  
      Examples:
      >>> n = 3, x = 1, y = 3
      [6,0,0]
      >>> n = 5, x = 2, y = 4
      [10,8,2,0,0]
      >>> n = 4, x = 1, y = 1
      [6,4,2,0]
  
      Constraints:
      2 <= n <= 100
      1 <= x, y <= n
      """
output:     distances = [[float('inf')] * n for _ in range(n)]
      for i in range(n):
          distances[i][i] = 0
          if i < n - 1:
              distances[i][i + 1] = 1
              distances[i + 1][i] = 1
      x -= 1
      y -= 1
      distances[x][y] = 1
      distances[y][x] = 1
  
      for k in range(n):
          for i in range(n):
              for j in range(n):
                  if distances[i][j] > distances[i][k] + distances[k][j]:
                      distances[i][j] = distances[i][k] + distances[k][j]
  
      count = [0] * (n - 1)
      for i in range(n):
          for j in range(i + 1, n):
              dist = distances[i][j]
              if 1 <= dist < n:
                  count[dist - 1] += 1
      
      return count