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
#gcdは3.4.3だとfractionsにある
from fractions import gcd

from math import factorial as f

from math import ceil,floor,sqrt

from sys import exit

from copy import deepcopy
import numpy as np

import bisect
import re


ii = lambda : int(input())
mi = lambda : map(int,input().split())
li = lambda : list(map(int,input().split()))



def main():

    n,x = mi()
    a = li()
    flag = [0 for i in range(n)]

    for i in range(1,n):
        if a[i-1] + x < a[i]:
            a[i] = min(a[i-1] + x,a[i])
            flag[i] = 1
    if a[n-1]+x<a[0]:
        a[0] = min(a[n-1]+x,a[0])
        flag[0] = 1
    for i in range(1,n):
        if a[i-1] + x < a[i]:
            a[i] = min(a[i-1] + x,a[i])
            flag[i] = 1
    if a[n-1]+x<a[0]:
        a[0] = min(a[n-1]+x,a[0])
        flag[0] = 1
    for i in range(1,n):
        if a[i-1] + x < a[i]:
            a[i] = min(a[i-1] + x,a[i])
            flag[i] = 1
    if a[n-1]+x<a[0]:
        a[0] = min(a[n-1]+x,a[0])
        flag[0] = 1

    a = a+a
    flag= flag+flag

    p = 0
    while(flag[p] == 1):
        p+=1
    po = p
    p+=1
    ans= 0
    maxpo = 0
    while(p < n or flag[p] == 1):
        if flag[p] == 0:
            ans+=a[po] * (p-po)
            maxpo = max(p-po-1,maxpo)
            po = p
        p+=1
    ans+=a[po] * (p-po)
    ans+=max(p-po-1,maxpo)*x





    print(ans)
            


main()
