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<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
typedef long long ll;
ll mini[2000];
int main()
{
	int num;
	ll gx;
	scanf("%d%lld",&num,&gx);
	vector<ll>v;
	for(int i=0;i<num;i++)
	{
		ll z;
		scanf("%lld",&z);
		v.push_back(z);
		mini[i]=z;
	}
	ll ans=1000000000000000000LL;
	for(int i=0;i<num;i++)
	{
		ll s=0;
		for(int j=0;j<num;j++)s+=mini[j];
		ans=min(ans,s+gx*i);
		for(int j=0;j<num;j++)mini[j]=min(mini[j],v[(j+num-i-1)%num]);
	}
	printf("%lld\n",ans);
}