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;
#define fo(i,a,b) for (int i = (a); i < (b); i++)
#define N 2345

int n;
long long a[N], x, ans = 1e18;
multiset<long long> v;
int main() {
	scanf("%d %lld", &n, &x);
	fo(i,0,n) scanf("%lld", a+i);
	fo(i,0,n) {
		long long res = i*x;
		v.clear();
		fo(j,0,i+1) v.insert(a[j]);
		fo(j,0,n) {
			res += *v.begin();
			v.erase(v.find(a[j]));
			v.insert(a[(j + i + 1)%n]);
		}

		ans = min(ans, res);
	}
	printf("%lld\n", ans);


	return 0;
}