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 math


N, X = map(int, input().split())
arr = list(map(int, input().split()))
"""
N, X = 2000, 1000
arr = []
for index in range(N):
    arr.append(randint(0,2000))
inventory = [] ## filled with indexes of arr to keep track
## im pretty sure that moving the prices is the same as moving the colour of the already had things
"""

## gaming time

def fastCosts(index, arr, N, X):
    ## dont I just need to add some constants to the list we already have
    costs = []
    ## what is each element of costs

    for counter in range(0, N):
        costs.append(arr[ (index-counter) % (N)] + counter*X)
    return costs

def elementWiseSum(list1, list2):
    if (len(list1) == 0):
        return list2
    if (len(list2) == 0):
        return list1
    for index in range(len(list1)):
        list1[index] += list2[index]
    return list1

def getAllCosts(arr, N, X):
    rtn = []
    for index in range(N):
        ##print(index)
        ##narr = copy.copy(arr)
        ##print(fastCosts(index, arr, N, X))

        #rtn = elementWiseSum(rtn, fastCosts(index,arr, N, X))
        rtn.append(fastCosts(index,arr, N, X))
    ##print(rtn)
    return rtn

def buyop(rtn, N, X):
    total = 0
    indexesGot = dict()
    for element in rtn:
        total += min(element)
        try:
            indexesGot[element.index(min(element))] += 1
        except:
            indexesGot[element.index(min(element))] = 1
    keys = indexesGot.keys()
    remove = 0
    ## corrections to our summation
    for key in keys:
        if (key != max(keys)):
            remove += indexesGot[key] * key * X
        elif (key == max(keys)):
            remove += (indexesGot[key] - 1) * key * X



    return total - remove

t = getAllCosts(arr, N, X)
print(buyop(t, N, X))
