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
from sys import stdin

def main():
    n,x=map(int,stdin.readline().split())
    cout=list(map(int,stdin.readline().split()))
    total=0
    nombreAttrape=[0]*n

    for i in range(n):
        depart=i
        minimum=cout[i]
        for j in range(1,n):
            indice=(i+j)%n
            nombre=n-j
            coutProchain=cout[indice]+x*nombre
            if minimum>coutProchain:
                depart=indice
                minimum=coutProchain
        nombreAttrape[depart]+=1

    nombreSort=max(nombreAttrape)-1
    for i in range(n):
        total+=cout[i]*nombreAttrape[i]
    total+=nombreSort*x

    print(total)
main()