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 <algorithm>
#include <climits>
#define N 2010
#define LL long long
using namespace std;

LL a[N];
LL b[N][N];
int main(int argc, char* argv[])
{
    LL n, x;
    while(cin >> n >> x) {
        for(int i = 0; i < n ; ++i ) {
            cin >> a[i];
        }
        for(int i = 0; i < n; ++i) {
            for(int j = 0; j < n; ++j) {
                if(j == 0) b[i][j] = a[i];
                else b[i][j] = min(b[i][j-1], a[(i + n - j) % n]);
            }
        }
        LL re = LLONG_MAX;
        for(int i = 0; i < n; ++i) {
            LL ans = i * x;
            for(int j = 0; j < n; ++j) {
                ans += b[j][i];
            }
            re = min(re, ans);
        }
        cout << re << endl;
    }
    return 0;