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 long long mod = 998244353;
const int N = 2222;
int n;
long long a[N];
long long x;
long long dp[N][N];
long long go(int i, int j) {
  if (j == n) {
    return 0;
  }
  long long ret = dp[i][j];
  if (ret != -1) return ret;
  ret = 1e18;
  if (i < n) {
    ret = min(ret, go(i + 1, j) + x);
  }
  if (i > 0) {
    ret = min(ret, go(i, j + 1) + a[i]);
  }
  return dp[i][j] = ret;
}
void solve() {
  cin >> n >> x;
  memset(dp, -1, sizeof dp);
  long long sum = 0;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i <= n; i++) sum += a[i];
  cout << min(sum, go(0, 0)) << endl;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
