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, i, m = 0, f = 0;
    long long s = 0;
    cin >> n >> x;
    int a[n], c[n] = {};
    for(i=0; i<n; i++){
        cin >> a[i];
    }
    while(f == 0){
        f = 1;
        for(i=0; i<n; i++){
            if(i == 0){
                if(a[0] > a[n-1] + x){
                    a[0] = a[n-1] + x;
                    c[0] = c[n-1] + 1;
                    m = max(m, c[0]);
                    f = 0;
                }
            }else{
                if(a[i] > a[i-1] + x){
                    a[i] = a[i-1] + x;
                    c[i] = c[i-1] + 1;
                    m = max(m, c[i]);
                    f = 0;
                }
            }
        }
    }
    s += (long long)m*(long long)x;
    for(i=0; i<n; i++){
        s += (long long)a[i] - (long long)c[i]*(long long)x;
    }
    cout << s;
    return 0;
}