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
#if !defined(__clang__) && defined(__GNUC__)
#include <bits/stdc++.h>
#else
#include <cstdlib>
#include <climits>
#include <iostream>
#include <cstdint>
#include <vector>
#include <string>
#include <complex>
#include <bitset>
#include <queue>
#include <deque>
#include <stack>
#include <utility>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <regex>
#endif //  !defined(__clang__) && defined(__GNUG__)
#include <boost/lexical_cast.hpp>
#include <boost/algorithm/string.hpp>
#include <boost/multi_array.hpp>
#include <boost/optional.hpp>
#include <boost/math/common_factor_rt.hpp>

using namespace std;

int main()
{
    int64_t N, X;
    std::cin >> N >> X;

    std::vector<int64_t> A;
    for (decltype(N) i = 0; i < N; ++i) {
        int64_t t;
        std::cin >> t;
        A.push_back(t);
    }

    int64_t ans = INT64_MAX;
    for (int64_t r = 0; r < N; ++r) {

        // r回転まで行う場合の個々の個体の最小要素
        int64_t s = 0;
        for (int64_t i = 0; i < N; ++i) {
            int64_t minorig = INT64_MAX;
            if (i < r) {
                minorig = *std::min_element(A.begin()+ N-(r-i), A.end());
                minorig = std::min(minorig, *std::min_element(A.begin(), A.begin()+i+1));
            }
            else {
                minorig = *std::min_element(A.begin()+ i - r, A.begin() + i+1);
            }
            s += minorig;
        }

        ans = std::min(ans, s + (r * X));
    }

    std::cout << ans << std::endl;

    return 0;
}
