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 collections import deque

class SlideMin:
    """
    スライド最小値\n
    各区間[ai, ai+leng]の最小値を取得する：O(n)\n
    self.que = [(i1, v1), (i2, v2), ..., (ik, vk)]\n
    i1 < ... < ik and v1 < ... < vk
    """
    def __init__(self, leng):
        self.que = deque([])
        self.leng = leng

    def top(self):
        return self.que[0]

    def getQue(self):
        return self.que

    def update(self, index, value):
        while self.que:
            if self.que[-1][1] >= value:
                self.que.pop()
            else:
                break

        self.que.append((index, value))

        if self.que[0][0] == index - self.leng:
            self.que.popleft()

N, X = map(int, input().split())
A = list(map(int, input().split()))

def sol(n):
    # n個前までの最小値
    B = A + A
    que = SlideMin(n + 1)
    ret = [10**18] * N
    for i, a in enumerate(B):
        que.update(i, a)
        ret[i % N] = min(ret[i % N], que.top()[1])
    return sum(ret) + n * X

ans = sum(A)
for i in range(N):
    ans = min(ans, sol(i))
print(ans)
