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<iostream>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f3f3f3f3f
ll a[2050];ll n;ll x;
ll cyz[2050];
int main(){
	std::ios::sync_with_stdio(false);
	cin>>n;cin>>x;
	for(int i=0;i<n;i++){
		cin>>a[i];cyz[i]=a[i];
	}
	ll minn=inf;ll res=0;
	for(int k=0;k<n;k++){
		ll temp=0;
		for(int i=0;i<n;i++){
			int pos=i-k;
			if(pos<0)pos=n+pos;
			cyz[i]=min(cyz[i],a[pos]);
			temp+=cyz[i];
		}
		temp+=x*k;
		minn=min(temp,minn);
	}
	cout<<minn<<endl;
}