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 <cstdio>
using namespace std;

typedef long long ll;
ll n, m, s, ans, mn[2005], a[2005];
int main()
{
	ll i, j;
	cin >> n >> m;
	for (i = 0; i < n; i++) {
		scanf ("%lld", &a[i]);
	}
	for (i = 0; i < n; i++) {
		mn[i] = 2e9;
	}
	for (i = 0; i < n; i++) {
		s = i * m;
		for (j = 0; j < n; j++) {
			mn[j] = min(mn[j], a[(i - j + n) % n]);
			s += mn[j];
		}
		if (i == 0 || s < ans) ans = s;
	}
	cout << ans;
    return 0;
}
