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 = 2e3 + 10;
long long n, x, ar[N], dp[N][N];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  for (long long i = 0; i < N; i++) fill(dp[i], dp[i] + N, (long long)1e9 + 10);
  cin >> n >> x;
  for (long long i = 0; i < n; i++) cin >> ar[i];
  dp[0][0] = 0;
  for (long long j = 1; j <= n; j++) dp[0][j] = ar[0] * j + x * (j - 1);
  for (long long i = 1; i < n; i++) {
    dp[i][0] = 0;
    for (long long j = 1; j <= n; j++) {
      dp[i][j] = dp[i - 1][j];
      for (long long k = 1; k <= j; k++)
        dp[i][j] = min(dp[i][j], dp[i - 1][j - k] + ar[i] * k + x * (k - 1));
    }
  }
  cout << dp[n - 1][n];
}
