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<algorithm>
#include<string>
#include<vector>
#define int long long
#define mod 1000000007
using namespace std;
int a[2345][2345], n, x, ans, cnt;
signed main() {
	cin >> n >> x;
	for (int i = 1; i <= n; i++) {
		cin >> a[i][0];
		ans += a[i][0];
	}
	for (int j = 1; j <= n; j++) {
		cnt = x * j;
		for (int i = 1; i <= n; i++) {
			int p = i - j; if (p <= 0)p += n;
			a[i][j] = min(a[i][j - 1], a[p][0]);
			cnt += a[i][j];
		}
		ans = min(ans, cnt);
	}
	cout << ans << endl;
}