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;
#define INF 1LL<<62
#define inf 1000000007

ll a[20002];
ll s[20002];
int main() {
	ll n,m;
	cin>>n>>m;
	for(ll i=0;i<n;i++){
		cin>>a[i];
	}
	ll ans=INF;
	for(ll i=0;i<n;i++){
		ll sum=i*m;
		for(ll j=0;j<n;j++){
			ll now=j+i;
			if(now>=n){
				now-=n;
			}
			if(s[j]==0){
				s[j]=a[now];
			}
			else if(s[j]>a[now]){
				s[j]=a[now];
			}
			sum+=s[j];
		}
		ans=min(sum,ans);
	}
	cout <<ans;
	// your code goes here
	return 0;
}