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;

int main() {
    int n, x; cin >> n >> x;
    vector<int> a(n, 0);
    for(int i = 0; i < n; ++i)
        cin >> a[i];
    
    int64_t ans = 1e9;
    ans = ans * ans;
    
    vector<vector<int>> partMin(n, vector<int> (n, 1e9 + 5));

    for(int i = 0; i < n; ++i) {
        partMin[i][i] = a[i];
        for(int j = i + 1; j < n; ++j)
            partMin[i][j] = min(a[j], partMin[i][j - 1]);
    }

    for(int slides = 0; slides < n; ++slides) {
        int64_t temp = 0;

        for(int i = 0; i < n; ++i) {
            int lf = i - slides;
            if(lf < 0)
                lf += n;
            int rt = i;
            if(lf <= rt) {
                temp += partMin[lf][rt];
            } else {
                temp += min(partMin[0][rt], partMin[lf][n - 1]);
            }
        }

        ans = min(ans, 1LL * slides * x + temp);
    }

    cout << ans << "\n";
}