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 lli long long int
#define REP(i,s,l) for(lli i=s;i<l;i++)
#define DEBUG 0
#define INF (1LL<<50)
#define MOD 1000000007

signed main(){

	lli n,x;
	cin>>n>>x;

	lli a[n],c[n];

	lli ans=0;
	for(lli i=0;i<n;i++){
		cin>>a[i];
		c[i] = a[i];
		ans += a[i];
	}

	for(lli t=1;t<n;t++){
		lli cost = t*x;
		for(lli i=0;i<n;i++){
			c[i] = min(c[i],a[(i+n-t)%n]);
			cost += c[i];
		}
		ans = min(ans,cost);
	}
	cout<<ans<<endl;

	return 0;
}