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>
const int dx[] = {1, 0, -1, 0};
const int dy[] = {0, -1, 0, 1};
using namespace std;
const int MAXN = 2222;
const long long INF = 1ll << 60;
int A[MAXN];
long long B[MAXN];
long long dp[MAXN];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, x;
  cin >> N >> x;
  for (int i = 0; i < N; i++) cin >> A[i];
  {
    int start = min_element(A, A + N) - A;
    for (int i = 0; i < N; i++) {
      B[i] = A[(i + start) % N];
    }
  }
  for (int i = 0; i <= N; i++) dp[i] = INF;
  dp[0] = 0;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j <= i; j++) {
      dp[i + 1] = min(dp[i + 1], dp[j] + B[j] + (B[j] + x) * (i - j));
    }
  }
  cout << dp[N] << endl;
  return 0;
}
