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>
#define f first 
#define s second 
#define pb push_back               
#define mp make_pair 

using namespace std;

const int mnx = 3e5 + 9;
const int mod = 1e9 + 7;

ll n, x, ans = 1e18;
ll a[mnx], b[mnx];

int main(){    

cin >> n >> x;

for(int i = 0; i < n; i++){
    cin >> a[i];
    b[i] = a[i];
}

for(int i = 0; i <= n; i++){
    ll cur = 0;
    for(int j = 0; j < n; j++){
        b[j] = min(b[j], a[(j - i + n) % n]);
        cur += b[j];
    }
    ans = min(ans, cur + i * x);
}

cout << ans;

return 0;

}
