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
#設定
import sys
input = sys.stdin.buffer.readline

#ライブラリインポート
from collections import defaultdict
INF = float("inf")

#入力受け取り
def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	N, x = getlist()
	a = getlist()
	B = [[INF] * N for i in range(N)]
	for i in range(N):
		B[0][i] = a[i]
	for i in range(1, N):
		for j in range(N):
			B[i][j] = min(B[i - 1][j], a[(j - i) % N])
	ans = INF
	for i in range(N):
		v = sum(B[i]) + i * x
		ans = min(ans , v)
	print(ans)

if __name__ == '__main__':
	main()