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;

long long n, x, s, mn=1e18, a[2005], m[2005];
int main() {
	int i, j;
	cin >> n >> x;
	for(j=0; j<n; j++) cin >> a[j], m[j] = 1e18;
	for(i=0; i<n; i++) {
		s = 0;
		for(j=0; j<n; j++) {
			m[j] = min(m[j], a[(j-i+n)%n]);
			s += m[j];
		}
		mn = min(mn, s + i*x);
	}
	cout << mn;
	return 0;
}
