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 -*-
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

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

catch_cnt = [0]*N
tmp_max_dist = 0
for i in range(N):
    dist = 0
    catch_ind = i
    tmp_max_cost = A[i]
    for j in range(1, N):
        prev_ind = (i-j) % N
        dist = j
        cost_catch_prev = A[prev_ind]+x*dist
        if tmp_max_cost > cost_catch_prev:
            tmp_max_cost = cost_catch_prev
            tmp_max_dist = max(tmp_max_dist, dist)
            catch_ind = prev_ind
    catch_cnt[catch_ind] += 1
ans = sum(a*b for a, b in zip(catch_cnt, A))+x*tmp_max_dist
print(ans)
