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 ll long long
ll b[2010],a[2010];
int main()
{
    ll i,j,k,m,n,x;
    ll cnt,ans=1ll * 2010 * 1e9;
    memset(a,0x3f,sizeof(a));
    cin>>n>>x;
    for(i=0; i<n; i++)
        cin>>b[i];
    for(i=0; i<n; i++)
    {
        cnt=0;
        for(j=0; j<n; j++)
            a[j]=min(a[j],b[(j-i+n)%n]);
        for(j=0; j<n; j++)
            cnt+=a[j];
        ans=min(ans,i*x+cnt);
    }
    cout<<ans<<endl;
    return 0;
}
