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;
using ll = long long;
const int inf = (int)1e9;
const int mod = (int)1e9 + 7;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};
int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int n;
  ll x;
  cin >> n >> x;
  ll a[n];
  for (int i = 0; i < (n); ++i) cin >> a[i];
  int min_index = 0;
  ll min_value = inf;
  for (int i = 0; i < (n); ++i) {
    if (a[i] < min_value) {
      min_value = a[i];
      min_index = i;
    }
  }
  bool get[n];
  get[min_index] = true;
  for (int i = 0; i < (n); ++i) {
    int index = i + min_index;
    if (get[index % n]) {
      if (a[(index + 1) % n] < a[index % n] + x) {
        get[(index + 1) % n] = true;
      } else {
        get[(index + 1) % n] = false;
        a[(index + 1) % n] = a[index % n] + x;
      }
    } else {
      if (a[(index + 1) % n] < a[index % n]) {
        get[(index + 1) % n] = true;
      } else {
        get[(index + 1) % n] = false;
        a[(index + 1) % n] = a[index % n];
      }
    }
  }
  ll sum = 0;
  for (int i = 0; i < (n); ++i) {
    sum += a[i];
  }
  cout << sum << endl;
  return 0;
}
