output_description: For each k=1, 2, ..., N-1 in this order, print a line containing the answer to
  the problem.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N X Y
attempt: def dijkstra(graph, start):
      ### initialize
      n_node = len(graph)
      d = [float("inf") for n in range(n_node)]
      d[start] = 0
      Q = [(_d, n) for _d, n in zip(d, range(n_node))]
      Q.sort()
  
      ### search
      while len(Q) != 0:
          u = Q[0][1]
          del Q[0]
          for v in range(n_node):
              if graph[u][v] == 1 and d[v] > d[u] + 1:
                  d[v] = d[u] + 1
      return d
  
  
  if __name__ == "__main__":
      N, X, Y = [int(i) for i in input().split()]
  
      ### graph making
      graph = [[0 for n in range(N)] for n in range(N)]
      graph[X - 1][Y - 1] = 1
      graph[Y - 1][X - 1] = 1
      for n in range(N - 1):
          graph[n][n + 1] = 1
          graph[n + 1][n] = 1
  
      ### call dijkstra
      l = []
      for n in range(N - 1):
          l.extend(dijkstra(graph, n)[n + 1 :])
      for n in range(1, N):
          print(l.count(n))
  
problem_description: Statement
  
  We have an undirected graph G with N vertices numbered 1 to N and N edges as
  follows:
  
    * For each i=1,2,...,N-1, there is an edge between Vertex i and Vertex i+1.
    * There is an edge between Vertex X and Vertex Y.
  
  For each k=1,2,...,N-1, solve the problem below:
  
    * Find the number of pairs of integers (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j in G is k.
samples: [{"input": "5 2 4", "output": "5\n    4\n    1\n    0\n    \n\nThe graph in this input is as follows:  \n  \n![Figure](https://img.atcoder.jp/ghi/3ae0885a4aeda99694b9fde4efe39dc1.png)  \n  \nThere are five pairs (i,j) (1 \\leq i < j \\leq N) such that the shortest\ndistance between Vertex i and Vertex j is 1:\n(1,2)\\,,(2,3)\\,,(2,4)\\,,(3,4)\\,,(4,5).  \nThere are four pairs (i,j) (1 \\leq i < j \\leq N) such that the shortest\ndistance between Vertex i and Vertex j is 2: (1,3)\\,,(1,4)\\,,(2,5)\\,,(3,5).  \nThere is one pair (i,j) (1 \\leq i < j \\leq N) such that the shortest distance\nbetween Vertex i and Vertex j is 3: (1,5).  \nThere are no pairs (i,j) (1 \\leq i < j \\leq N) such that the shortest distance\nbetween Vertex i and Vertex j is 4.\n\n* * *"}, {"input": "3 1 3", "output": "3\n    0\n    \n\nThe graph in this input is as follows:  \n  \n![Figure](https://img.atcoder.jp/ghi/be2921b3b307fc993a390a59437e624e.png)  \n  \n\n* * *"}, {"input": "7 3 7", "output": "7\n    8\n    4\n    2\n    0\n    0\n    \n\n* * *"}, {"input": "10 4 8", "output": "10\n    12\n    10\n    8\n    4\n    1\n    0\n    0\n    0"}]