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


#st = time.time()
#N = 2000
#m = 1000000000
#x = np.random.randint(m)
#A = np.random.randint(m,size=(N))

a = map(int,raw_input().split())
N = a[0]
x = a[1]
A = map(int,raw_input().split())

B = np.zeros(N)
E = np.zeros(N)
C = 10000000000*np.ones((N,N))
for idx in xrange(N):
  for i in xrange(N):
    if x*i > A[idx]:
      break
    C[idx][i] = A[idx-i]+x*i
  i = np.where(C[idx]==min(C[idx]))[0][0]
  B[idx] = A[idx-i]
  E[idx] = i

print int(sum(B)+max(E)*x)