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>
template <typename T>
void Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void Scan(First& first, Rest&... rest) {
  std::cin >> first;
  Scan(rest...);
}
using ll = long long;
using ull = unsigned long long;
constexpr int INFINT = 1 << 30;
constexpr ll INFLL = 1LL << 60;
constexpr double EPS = 0.0000000001;
constexpr int MOD = 1000000007;
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  int n, x;
  Scan(n, x);
  ;
  std::vector<ll> a(n);
  for (auto& i : a) std::cin >> i;
  ;
  std::vector<ll> ansVec(a);
  ll ans = 0;
  int magicCnt = 0;
  for (int i = 0; i < int(n); ++i) {
    ll min = a[i];
    for (int j = (1); j < (n); ++j) {
      if (ansVec[i] > a[(i - j + n) % n] + x * j) {
        ansVec[i] = a[(i - j + n) % n] + x * j;
        min = std::min(min, a[(i - j + n) % n]);
        magicCnt = std::max(magicCnt, j);
      }
    }
    ans += min;
  }
  std::cout << ans + x * magicCnt;
  std::cout << "\n";
  ;
  return 0;
}
