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 "testlib.h"
#include <bits/stdc++.h>

using namespace std;

using ll = long long;

const int MX = 2007;

int a[MX];
int cost[MX];

int main() {
#ifdef BZ
    freopen("input.txt", "r", stdin);
#endif
    ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
    int n;
    cin >> n;
    int x;
    cin >> x;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cost[i] = a[i];
    }
    ll ans = 1e18;
    for (int i = 0; i <= n + 1; i++) {
        ll cans = 0;
        for (int j = 0; j < n; j++) {
            cost[j] = min(cost[j], a[(i + j) % n]);
            cans += cost[j];
        }
        ans = min(ans, cans + 1ll * x * i);
    }
    cout << ans << "\n";
}


