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<cstdio>
#include<algorithm>
using namespace std;

long long N, x, a[2000], b[2000];

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

    long long ans = 100000000000000;
    for(int k = 0; k < N; k++){
        long long tmp = k*x;
        for(int i = 0; i < N; i++){
            tmp += b[i];
            b[i] = min(b[i], a[(i+N-(k+1))%N]);
        }
        ans = min(ans, tmp);
        
    }
    cout << ans << endl;
}