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 A, size_t N, typename T>
void Fill(A (&array)[N], const T& val) {
  std::fill((T*)array, (T*)(array + N), val);
}
const int MAX = 510000;
const int MOD = 1000000007;
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
class Monoid {
 public:
  int unit;
  Monoid() { unit = 1e9 + 7; }
  int calc(int a, int b) { return min(a, b); }
};
class SegmentTree {
 public:
  int n;
  vector<int> tree;
  Monoid mono;
  SegmentTree(vector<int>& v) {
    n = 1 << (int)ceil(log2(v.size()));
    tree = vector<int>(n << 1);
    for (int i = 0; i < v.size(); i++) {
      update(i, v[i]);
    }
    for (int i = v.size(); i < n; i++) {
      update(i, mono.unit);
    }
  }
  void update(int k, int x) {
    k += n;
    tree[k] = x;
    for (k = k >> 1; k > 0; k >>= 1) {
      tree[k] = mono.calc(tree[k << 1 | 0], tree[k << 1 | 1]);
    }
  }
  int query(int l, int r) {
    int res = mono.unit;
    l += n;
    r += n;
    while (l < r) {
      if (l & 1) {
        res = mono.calc(res, tree[l++]);
      }
      if (r & 1) {
        res = mono.calc(res, tree[--r]);
      }
      l >>= 1;
      r >>= 1;
    }
    return res;
  }
};
int q, cnt = 0, a, b, t, c, x, ans = 0, sum = 0;
int main(void) {
  int n;
  cin >> n >> x;
  vector<int> a(n * 2);
  for (int i = 0; i < (int)(n); i++) cin >> a[i], a[i + n] = a[i];
  SegmentTree sg(a);
  ans = 1 << 30;
  for (int i = 0; i < (int)(n); i++) {
    cnt = i * x;
    for (int j = 0; j < (int)(n); j++) cnt += sg.query(j, j + i + 1);
    chmin(ans, cnt);
  }
  cout << ans << endl;
}
