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 "bits/stdc++.h"

using namespace std;

void solve()
{
	int n;
	long x;
	cin >> n >> x;
	vector<long> as(n);
	long ans = 0;
	for (int i = 0; i < n; i++)
	{
		cin >> as[i];
		ans += as[i];
	}

	for (int i = 1; i < n; i++)
	{
		long tmp = i*x;
		vector<long> bs = as;
		for (int j = 0; j < n; j++)
		{
			bs[j] = min(bs[j], as[(j-1+n)%n]);
			tmp += bs[j];
		}
		ans = min(ans, tmp);
		swap(as, bs);
	}
	cout << ans << endl;
}

int main()
{
	solve();
	//cout << "yui(*-v・)yui" << endl;
	return 0;
}
