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;
int n;
long long aa[2020];
long long x;
long long a[2020];
long long sol(int dmax) {
  long long dp[2020];
  dp[n] = 0;
  for (int i = 0; i < n; i++) dp[i] = (1LL << 60);
  for (int i = n - 1; i >= 0; i--) {
    for (int d = 1; d <= dmax && i + d <= n; d++)
      dp[i] = min(dp[i], dp[i + d] + a[i] * d);
  }
  return dp[0] + x * (dmax - 1);
}
int main() {
  scanf("%d", &n);
  scanf("%lld", &x);
  for (int i = 0; i < n; i++) scanf("%lld", &aa[i]);
  long long mini = 1LL << 60;
  for (int i = 0; i < n; i++) mini = min(mini, aa[i]);
  for (int i = 0; i < n; i++) {
    if (aa[i] == mini) {
      for (int j = 0; j < n; j++) a[j] = aa[(i + j) % n];
      break;
    }
  }
  long long ans = (1LL << 60);
  ans = min(ans, sol(1));
  ans = min(ans, sol(n));
  int lb = 1, ub = n - 1;
  for (; ub - lb > 1;) {
    int mid = (ub + lb) / 2;
    long long s = sol(mid), t = sol(mid + 1);
    if (s > t) {
      ans = min(ans, t);
      lb = mid;
    } else {
      ans = min(ans, s);
      ub = mid;
    }
  }
  printf("%lld\n", ans);
}
