output_description: Find the minimum time that Snuke needs to have slimes in all N colors.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N x
      a_1 a_2 ... a_N
attempt: import sys
  from collections import defaultdict as dd
  
  input = sys.stdin.readline
  N, x = map(int, input().split())
  a = list(map(int, input().split()))
  res = float("inf")
  import heapq
  
  
  class prim:
      def __init__(self, n, e):
          self.e = e
          self.n = n
  
      def MSTcost(self):
          h = []
          visited = [0] * (self.n + 1)
          ks = list(self.e.keys())
          b = pow(10, 10)
          for edge in self.e[ks[0]]:
              heapq.heappush(h, edge[1] * b + edge[0])
          res = 0
          visited[ks[0]] = 1
          while len(h):
              p = heapq.heappop(h)
              p0 = p // b
              p1 = p % b
              if visited[p1]:
                  continue
              visited[p1] = 1
              for q in self.e[p1]:
                  if visited[q[0]]:
                      continue
                  heapq.heappush(h, q[1] * b + q[0])
              res += p0
          return res
  
  
  e = dd(list)
  for k in range(N + 1):
      for i in range(N):
          e[N].append(((i + k) % N, a[i]))
      pri = prim(N, e)
      res = min(res, pri.MSTcost() + k * x)
  print(res)
  
problem_description: Statement
  
  Snuke lives in another world, where slimes are real creatures and kept by some
  people. Slimes come in N colors. Those colors are conveniently numbered 1
  through N. Snuke currently has no slime. His objective is to have slimes of
  all the colors together.
  
  Snuke can perform the following two actions:
  
    * Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
  
    * Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
  
  Find the minimum time that Snuke needs to have slimes in all N colors.
samples: [{"input": "2 10\n    1 100", "output": "12\n    \n\nSnuke can act as follows:\n\n  * Catch a slime in color 1. This takes 1 second.\n  * Cast the spell. The color of the slime changes: 1 \u2192 2. This takes 10 seconds.\n  * Catch a slime in color 1. This takes 1 second.\n\n* * *"}, {"input": "3 10\n    100 1 100", "output": "23\n    \n\nSnuke can act as follows:\n\n  * Catch a slime in color 2. This takes 1 second.\n  * Cast the spell. The color of the slime changes: 2 \u2192 3. This takes 10 seconds.\n  * Catch a slime in color 2. This takes 1 second.\n  * Cast the soell. The color of each slime changes: 3 \u2192 1, 2 \u2192 3. This takes 10 seconds.\n  * Catch a slime in color 2. This takes 1 second.\n\n* * *"}, {"input": "4 10\n    1 2 3 4", "output": "10\n    \n\nSnuke can act as follows:\n\n  * Catch a slime in color 1. This takes 1 second.\n  * Catch a slime in color 2. This takes 2 seconds.\n  * Catch a slime in color 3. This takes 3 seconds.\n  * Catch a slime in color 4. This takes 4 seconds."}]