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 bisect
import heapq
import itertools
import math
import operator
import os
import re
import string
import sys
from collections import Counter, deque, defaultdict
from copy import deepcopy
from decimal import Decimal
from fractions import gcd
from functools import lru_cache, reduce
from operator import itemgetter, mul, add, xor

import numpy as np

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 = np.array(A, dtype=int)
# xs[i]: i にするまでに色を変える回数
xs = np.zeros(N, dtype=int)
for i in range(N * 3):
    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 = dp.sum() + xs.max() * X
print(ans)
