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
# coding:utf-8

import sys

INF = float('inf')
MOD = 10 ** 9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()


def main():
    n, x = LI()
    A = LI()

    min_a, min_i = INF, -1
    res = 0
    for i, a in enumerate(A):
        if a < min_a:
            min_a = a
            min_i = i
        res += a
    A = A[min_i:] + A[:min_i]

    dp = [INF] + A
    for k in range(n - 1):
        tmp = 0
        for i in range(n)[::-1]:
            if dp[i + 1] > dp[i] + x:
                dp[i + 1] = dp[i]
            tmp += dp[i + 1]

        res = min(res, tmp + (k + 1) * x)

    return res


print(main())
