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