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;

const int N = 2000 + 7;

pair < long long, long long > w[N][N];
long long res, x, n, a[N];
long long dis[N];

long long main() {
	cin >> n >> x;
	for (long long i = 1; i <= n; i++)	
		cin >> a[i];
	for (long long i = 1; i <= n; i++) {
		for (long long j = 1; j <= n; j++) {
			if (j >= i) 
				w[i][j] = {a[i] + (j - i) * x, j - i};
			else
				w[i][j] = {a[i] + (j + n - i) * x, j + n - i};	
		}
	}	
	long long maxd = 0;
	for (long long i = 1; i <= n; i++) {
		long long mn = w[1][i].first, d = i - 1;
		for (long long j = 1; j <= n; j++) {
			if (w[j][i].first < mn)
				mn = w[j][i].first, d = w[j][i].second;
		//	cout << j << " " << i << " " << w[j][i].first << endl;
		}
		maxd = max(d, maxd);
		res += mn - d * x; 
	}	
	cout << res + maxd * x;
	return 0;
}













