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;
void faster() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
const long long INF = 1e9;
const long long MOD = 1e9 + 7;
const long long MAXN = 3e5 + 123;
const long double EPS = 1e-12;
const int dx[4] = {-1, 0, 0, 1};
const int dy[4] = {0, -1, 1, 0};
long long n, x, a[MAXN], mn = INF, ans;
void solve() {
  cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    mn = min(a[i], mn);
  }
  x += mn;
  for (int i = 0; i < n; ++i) {
    ans += min(x, a[i]);
  }
  cout << ans;
}
int main() {
  faster();
  int T = 1;
  while (T--) {
    solve();
  }
  return 0;
}
