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
//魔法をかける回数を固定(Kに)する。すると、色iのスライムは色i～i-Kのスライムから作れる。
//魔法によるコストは同じなので、この中から最小のものを選べばよい。
//愚直にやると、魔法回数O(N), 色O(N), 最小値O(N)だが、ナイーブに更新すると最小値クエリO(1)になって間に合う。

#include <iostream>
#include <string>
#include <algorithm>
#include <functional>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#define int long long
using namespace std;

int n, x;
int a[2000];

signed main() {
	int i, j, k;
	
	cin >> n >> x;
	for (i = 0; i < n; i++) cin >> a[i];
	
	int ans = 11451419198100721;
	int mini[2000];
	for (i = 0; i < n; i++) mini[i] = 1145141919;
	
	//魔法をi回かける
	for (i = 0; i < n; i++) {
		int cst = 0;
		//スライムjを得るためのコスト（魔法コストを除く）
		for (j = 0; j < n; j++) {
			mini[j] = min(a[(j - i + n) % n], mini[j]);
			cst += mini;
		}
		ans = min(ans, cst + i * x);
	}
	cout << ans << endl;
	return 0;
}