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>
using namespace std;
void solve();
int main (){ 
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    int t;
    t = 1;
    for (int i = 0; i < t; i++) solve();
    
}
void solve() {
    //catch slimes he does not have if time required is less than x
    //if min cost of catching a new slime < min cost of catching any slime + move cost, then catch
    //Else, transform slime.
    int time = 0;
    int n,x;
    cin >> n >> x;
    int a[n];
    for (int i = 0; i < n; i++) cin >> a[i];
    int caught[n] = {0};
    int total_min = *(min_element(a,a + n - 1));
    while (1) {
        //loop through slimes and catch ones that satisfy the condition
        for (int i = 0; i < n; i++) {
            if (a[i] < total_min + x && !caught[i]) {
                caught[i]++;
                time += a[i];
            }
        }
        //cout << "array is " << caught[0] << ' ' << caught[1] << endl;
        //if all caught do nothing
        //cout << "min element is " << *(min_element(caught,caught + n)) << *(caught + n - 1 )<< '\n';
        if (*(min_element(caught,caught + n )) >= 1) break;
        //Do spell (isn't working because it's moving the slime change all the way through the cycle)
        time += x;
        int prevcot = 0;
        for (int i = 0; i < n; i++) {
            if (i == n - 1) {
                if ((caught[n - 1] && !prevcot) || caught[n-1] > 1) {
                    caught[n - 1]--;
                    caught[0]++;
                    prevcot = 1;
                }
            } else {
                if ((caught[i] && !prevcot) || caught[i] > 1) {
                    caught[i]--;
                    caught[i + 1]++;
                    prevcot = 1;
                } else {
                    prevcot = 0;
                }
            }
        }
        //cout << "array is " << caught[0] << ' ' << caught[1] << endl;
    }
    cout << time;

}