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
#include <iostream>
#include <set>
using namespace std;

const int MAXN = 1e5 + 10;
long long x, ans, n, a[MAXN];

int main() {
	cin >> n >> x;
	for (int i = 0; i < n; i++)
		cin >> a[i], ans += a[i];
	for (int k = 1; k < n; k++) {
		multiset<int> r;
		for (int i = 0; i < k; i++)
			r.insert(a[i]);
		long long res = 0;
		for (int i = k, z = 0; z < n; z++, i++) {
			i %= n;
			r.insert(a[i]);
			res += *r.begin();
			r.erase(r.find(a[(i - k + n) % n]));
		}
		ans = min(ans, res + k * x);
	}
	cout << ans;
}