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 sys
import heapq
from operator import itemgetter
from collections import deque, defaultdict
from bisect import bisect_left, bisect_right
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)


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

    minCatch = 0
    for i, a in enumerate(A):
        if A[minCatch] > a:
            minCatch = i

    magicCount = [0] * N
    minCost = [float('inf')] * N
    minCost[minCatch] = A[minCatch]

    for i in range(1, N + 1):
        j = (i + minCatch) % N
        if A[j] > minCost[j - 1] + X:
            minCost[j] = minCost[j - 1] + X
            magicCount[j] = magicCount[j - 1] + 1
        else:
            minCost[j] = A[j]
            magicCount[j] = 0

    ans = 0
    for cost, magic in zip(minCost, magicCount):
        ans += cost - magic * X
    ans += max(magicCount) * X
    print(ans)

sol()