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>
using namespace std;

typedef unsigned long long ull;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);

	int N, x;
	int a[2000];
	int b[2000];

	cin >> N >> x;
	for(int i=0; i<N; i++) cin >> a[i];

	ull res = 0;
	for(int i=0; i<N; i++){
		res += a[i];
	}

	for(int m=1; m<N; m++){
		ull tot = m * x;
		for(int i=0; i<N; i++){
			b[i] = min(a[i], a[(i-1+N) % N]);
			tot += b[i];
		}
		for(int i=0; i<N; i++) a[i] = b[i];
		res = min(res, tot);
	}
	cout << res << endl;
	return 0;
}
