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>

#include <boost/range/adaptors.hpp>
#include <boost/range/irange.hpp>

using namespace std;
using namespace boost;
using namespace boost::adaptors;

int main() {
    int64_t n, x;
    cin >> n >> x;

    vector<int64_t> a(n);
    for (auto&& aa : a) {
        cin >> aa;
    }

    int64_t ans = 1L << 50;
    for (auto i : irange(0L, n)) {
        int64_t s = accumulate(a.begin(), a.end(), 0L);
        ans = min(s + i * x, ans);

        auto aa = a[n - 1];
        for (auto j : irange(1L, n)) {
            a[j] = min(a[j], a[j - 1]);
        }
        a[0] = min(a[0], aa);
    }

    cout << ans << endl;
}