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;
using ll = long long;

int main() {
    ll N, X;
    cin >> N >> X;
    vector<ll> A(N), B(N);
    ll minv = 0;
    for (auto &e : A) { cin >> e; minv += e; }
    for (int i = 1; i < N; i++) {
        ll sum = 0;
        for (int j = 0; j < N; j++) B[(j+1)%N] = min(A[(j+1)%N], A[j]), sum += B[(j+1)%N];
        A = B;
        minv = min(minv, sum + i * X);
    }
    cout << minv << endl;
    return (0);
}
