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;
template <typename T1, typename T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T1, typename T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
inline template <typename T>
T up(const T& l, const T& r) {
  T res;
  res = min<T>(l, r);
  return res;
}
inline template <typename T>
class SegmentTree {
 public:
  vector<T> seg;
  int sz = 1;
  T unit;
  SegmentTree(int n, T unit = 0) {
    this->unit = unit;
    while (sz < n) sz <<= 1;
    seg.resize(sz * 2, unit);
  }
  void set(const int& k, const T& x) { seg[sz - 1 + k] = x; }
  T get(const int& k) { return seg[sz - 1 + k]; }
  void update(int k, const T& v) {
    k += sz - 1;
    seg[k] = v;
    while (k > 0) {
      k = (k - 1) / 2;
      seg[k] = up(seg[2 * k + 1], seg[2 * k + 2]);
    }
  }
  T query(int a, int b, int k, int l, int r) {
    if (r <= a || b <= l) {
      return unit;
    }
    if (a <= l && r <= b) {
      return seg[k];
    } else {
      T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
      T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
      return up(vl, vr);
    }
  }
};
int main() {
  int n;
  long long x;
  cin >> n >> x;
  vector<long long> a(n * 2);
  for (long long i = 0; i < (long long)(n); i++) {
    cin >> a[i];
    a[i + n] = a[i];
  }
  SegmentTree<long long> sg(n * 2, LLONG_MAX);
  for (int i = 0; i < (int)(n); i++) {
    sg.update(i, a[i]);
    sg.update(i + n, a[i + n]);
  }
  long long res = LLONG_MAX;
  for (int k = 0; k < (int)(n); k++) {
    long long cost = k * x;
    int sz = sg.sz;
    for (int j = 0; j < (int)(n); j++) {
      if (j - k < 0) {
        cost += sg.query(j - k + n, j + 1 + n, 0, 0, sz);
      } else {
        cost += sg.query(j - k, j + 1, 0, 0, sz);
      }
    }
    chmin(res, cost);
  }
  cout << res << "\n";
  return 0;
}
