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 os
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7

N, X = list(map(int, sys.stdin.readline().split()))
A = list(map(int, sys.stdin.readline().split()))

# dp[i]: i 色のスライムを捕まえるコスト
dp = A[:]
# xs[i]: i にするまでに色を変える回数
xs = [0] * N
for i in range(N ** 2):
    i = i % N
    j = (i + 1) % N
    if dp[i] + xs[i] * X + X <= dp[j] + xs[j] * X:
        dp[j] = dp[i]
        xs[j] = xs[i] + 1
# いい感じに順番をつければ色変えは最大 xs.max() 回でいい
ans = sum(dp) + max(xs) * X
print(ans)
