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;
typedef long long LL;
int a[2005], mn[2005], idx[2005];
int main(){
	int n, x;
	scanf("%d%d", &n, &x);
	for(int i=1;i<=n;i++){
		scanf("%d", &a[i]);
		idx[i] = i;
		mn[i] = a[i];
	}
	LL ans = 1e18;
	for(int i=0;i<=n-1;i++){
		LL res = (LL)i*x;
		for(int j=1;j<=n;j++){
			mn[j] = min(mn[j], a[idx[j]]);
			res += mn[j];
			idx[j]--;
			if(idx[j] == 0) idx[j] = n;
		}
		ans = min(ans, res);
	}
	printf("%lld\n", ans);
}