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 <class T>
bool chmax(T &a, const T &b) {
  return (a < b) ? (a = b, 1) : 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  return (b < a) ? (a = b, 1) : 0;
}
using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
const double EPS = 1e-10;
const double PI = acos(-1.0);
const ll inf = 1LL << 62;
const ll mod = 1000000007LL;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
ll extgcd(ll a, ll b, ll &x, ll &y) {
  x = 1, y = 0;
  ll g = a;
  if (b != 0) g = extgcd(b, a % b, y, x), y -= a / b * x;
  return g;
}
ll ADD(const ll &a, const ll &b, const ll &mod) { return (a + b) % mod; }
ll SUB(const ll &a, const ll &b, const ll &mod) { return (a - b + mod) % mod; }
ll MUL(const ll &a, const ll &b, const ll &mod) { return (1LL * a * b) % mod; }
ll DIV(const ll &a, const ll &b, const ll &mod) {
  ll x, y;
  extgcd(b, mod, x, y);
  return MUL(a, (x + mod) % mod, mod);
}
random_device rd;
mt19937 mt(rd());
uniform_int_distribution<int> dice(1, 6);
uniform_real_distribution<double> score(0.0, 10.0);
int main(void) {
  int n;
  cin >> n;
  ll x;
  cin >> x;
  vll a(n);
  for (auto &e : a) cin >> e;
  int mi = min_element(begin(a), end(a)) - begin(a);
  ll res = 0LL;
  ll cmin = a[mi];
  int cnt = 0;
  for (int i = (int)(1); i < (int)(n + 1); ++i) {
    int ci = (mi + i) % n;
    int pi = (ci - 1 + n) % n;
    if (i == n) {
      res += cnt * x + (cnt + 1) * cmin;
      break;
    }
    if (chmin(a[ci], a[pi] + x)) {
      cnt++;
    } else {
      cnt = 0;
      res += cnt * x + (cnt + 1) * cmin;
      cmin = a[ci];
    }
  }
  cout << res << endl;
  return 0;
}
