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;

typedef long long ll;
const int N = 2005;
const int M = 1000000007;

int n;
ll x;
ll dp[N][N];

int main() {
  while (~scanf("%d%I64d", &n, &x)) {
    for (int i = 0; i < n; i++) {
      scanf("%I64d", &dp[i][0]);
    }
    for (int i = 0; i < n; i++) {
      for (int j = 1; j < n; j++) {
        dp[i][j] = min(dp[i][j - 1], a[(i - j + n) % n]);
      }
    }
    for (int j = 0; j < n; j++) {
      for (int i = n - 1; i >= 0; i--) {
        dp[i][j] += dp[i + 1][j];
      }
    }
    ll ans = 0x3f3f3f3f3f3f3f3fll;
    for (int j = 0; j < n; j++) {
      ans = min(ans, j * x + dp[0][j]);
    }
    printf("%I64d\n", ans);
  }
}
