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 N = 4007;
const long long INF = 1e18 + 239;
long long n, x;
long long a[N];
long long dp[N][N];
void init() {
  for (long long i = 0; i < N; i++) {
    for (long long j = 0; j < N; j++) {
      dp[i][j] = INF;
    }
  }
  for (long long i = 0; i < n; i++) {
    dp[i][i] = a[i];
  }
}
long long get(long long l, long long r) {
  if (dp[l][r] == INF) {
    dp[l][r] = min(dp[l][r], get(l, r - 1) + a[r]);
    dp[l][r] = min(dp[l][r], a[l] + get(l, r - 1) + x);
  }
  return dp[l][r];
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> x;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (long long i = 0; i < n; i++) {
    a[i + n] = a[i];
  }
  n *= 2;
  init();
  long long ans = INF;
  for (long long i = 0; i < n / 2; i++) {
    ans = min(ans, get(i, i + n / 2 - 1));
  }
  cout << ans << endl;
}
