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 N;
ll a[2005];ll x;ll dp[2005][2005];ll sum=1ll<<60ll;
int main(){
	cin>>N>>x;

	for(int i=1;i<=N;i++){
		cin>>a[i];
	}
	for(int i=1;i<=N;i++){
		dp[i][0]=a[i];
	
	for(int j=1;j<=N;j++){
		int pos=i-j;
		if(pos<=0)pos=N-abs(pos);
		dp[i][j]=min(dp[i][j-1],a[pos]);

	}
}

for(int i=0;i<=N-1;i++){
	ll ans=0;
	for(int j=1;j<=N;j++){
		ans+=dp[j][i];
		
	}
	sum=min(sum,ans+i*x);
}
	cout<<sum<<endl;
}
