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;
const int N = 2 * 1000 + 10;
long long n, x;
long long cost[N], DP[N];
long long KeepMin[N][N];
void input() {
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> cost[i];
  return;
}
int GetMin(int a, int b) {
  if (a - b < 0) return min(KeepMin[0][a + 1], KeepMin[n - b][n]);
  return KeepMin[a - b][a + 1];
}
void PrePros() {
  for (int i = 0; i < n; i++) KeepMin[i][i + 1] = cost[i];
  for (int l = 2; l <= n; l++)
    for (int i = 0; i + l <= n; i++)
      KeepMin[i][i + l] = min(KeepMin[i + 1][i + l], cost[i]);
  return;
}
void solve() {
  PrePros();
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) DP[i] += GetMin(j, i);
  return;
}
void output() {
  long long ans = DP[0];
  for (int i = 0; i < n; i++) ans = min(DP[i] + i * x, ans);
  cout << ans << endl;
  return;
}
int main() {
  input();
  solve();
  output();
  return 0;
}
