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>
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define inf (int)1e18
int n,x,a[2005],dp[2005];
int recurse(int i,int n)
{
    if(i==n)
        return 0;

    if(dp[i]!=-1)
        return dp[i];
    int ans=inf;
    for(int j=0;i+j<n;j++)
    {
        ans=min(ans,max((j+1)*a[i]+j*x,recurse(i+j+1,n)));
    }
    //dp[i]=ans;
    return dp[i]=ans;
}
main()
{
    int i;
    cin>>n>>x;

    for(i=1;i<=n;i++)
        cin>>a[i];
    memset(dp,-1,sizeof(dp));
    int ans=recurse(1,n+1);
   // cout<<recurse(0,n)<<endl;
    memset(dp,-1,sizeof(dp));
    a[n+1]=a[1];


    ans=min(ans,recurse(2,n+2));
    a[0]=a[n];
    memset(dp,-1,sizeof(dp));
    ans=min(ans,recurse(0,n));


    //cout<<recurse(1,n+1)<<endl;


    cout<<ans;
    return 0;
}
