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 i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using f64 = double;
using f80 = long double;
using pii = pair<i32, i32>;
using vi32 = vector<i32>;
using vu32 = vector<u32>;
using vi64 = vector<i64>;
using vu64 = vector<u64>;
using vf64 = vector<f64>;
using vf80 = vector<f80>;
using vstr = vector<string>;
using vpii = vector<pii>;
using vvi32 = vector<vi32>;
using vvu32 = vector<vu32>;
using vvi64 = vector<vi64>;
using vvu64 = vector<vu64>;
using vvf64 = vector<vf64>;
using vvf80 = vector<vf80>;
template <typename T, typename S>
bool amax(T &x, S y) {
  if (x < y) {
    x = y;
    return 1;
  }
  return 0;
}
template <typename T, typename S>
bool amin(T &x, S y) {
  if (y < x) {
    x = y;
    return 1;
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(16);
  cerr << fixed << setprecision(16);
  u64 n, x;
  cin >> n >> x;
  vu64 a(n);
  for (int i = 0; i < (n); i++) cin >> a[i];
  u64 sum = a[0];
  u64 c = 1, max_c = 0;
  for (int i = 1; i <= (n - 1); i++) {
    if (a[i] > sum + x * c) {
      a[i] = sum;
      amax(max_c, c);
      c++;
    } else {
      sum = a[i];
      c = 1;
    }
  }
  if (a[0] > sum + x * c) {
    a[0] = sum;
    amax(max_c, c);
    c++;
    for (int i = 1; i <= (n - 1); i++) {
      if (a[i] > sum + x * c) {
        a[i] = sum;
        amax(max_c, c);
        c++;
      } else {
        sum = a[i];
        c = 1;
      }
    }
  }
  u64 ans = accumulate((a).begin(), (a).end(), 0ull);
  ans += x * max_c;
  cout << ans << endl;
  return 0;
}
