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.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

The input is given from Standard Input in the following format:


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
import numpy as np


tflag = False
if tflag:
  N = 2000
  m = 1000000000
  x = np.random.randint(m)
  A = np.random.randint(m,size=(N))
#  st = time.time()
else:
  a = map(int,raw_input().split())
  N = a[0]
  x = a[1]
  A = map(int,raw_input().split())

E = np.zeros(N)
B = 1000000000*np.ones((N,N))
B[0] = np.array(A)
E[0] = sum(B[0])
for idx in xrange(1,N):
  B[idx] = np.array([min(B[idx-1][i], A[i-idx]) for i in range(N)])
  E[idx] = sum(B[idx])+idx*x

print int(min(E))