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 int Maxn = 10000 + 100;
int N;
long long M;
long long A[Maxn], Cnt[Maxn];
inline int pre(int x) {
  if (x == 1) return N;
  return x - 1;
}
int main() {
  scanf("%d%lld", &N, &M);
  for (int i = 1; i <= N; ++i) scanf("%lld", &A[i]);
  long long Ans = 0;
  for (int i = 1; i <= N; ++i) {
    long long Sum = 0x3f3f3f3f3f3f3f;
    long long tot = -1, k = 0;
    int fl = 0;
    for (int j = i;; j = pre(j)) {
      if (j == i && fl) break;
      fl = 1;
      ++tot;
      if (tot * M + A[j] < Sum) Sum = tot * M + A[j], k = tot;
    }
    Cnt[k]++;
    Ans += Sum;
  }
  for (int i = 1; i <= N; ++i)
    if (Cnt[i]) Ans -= (long long)(M * i * (Cnt[i] - 1));
  cout << Ans << endl;
  return 0;
}
