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;
inline bool SR(int &x) { return scanf("%d", &x) == 1; }
inline bool SR(long long &x) { return scanf("%lld", &x) == 1; }
inline bool SR(double &x) { return scanf("%lf", &x) == 1; }
inline bool SR(char *s) { return scanf("%s", s) == 1; }
inline bool RI() { return true; }
template <typename I, typename... T>
inline bool RI(I &x, T &...tail) {
  return SR(x) && RI(tail...);
}
inline void SP(const int x) { printf("%d", x); }
inline void SP(const long long x) { printf("%lld", x); }
inline void SP(const double x) { printf("%.16lf", x); }
inline void SP(const char *s) { printf("%s", s); }
inline void PL() { puts(""); }
template <typename I, typename... T>
inline void PL(const I x, const T... tail) {
  SP(x);
  if (sizeof...(tail)) putchar(' ');
  PL(tail...);
}
template <typename I>
void _DOING(const char *s, I &&x) {
  cerr << s << " = " << x << endl;
}
template <typename I, typename... T>
void _DOING(const char *s, I &&x, T &&...tail) {
  int c = 0;
  while (*s != ',' || c != 0) {
    if (*s == '(' || *s == '[' || *s == '{') c++;
    if (*s == ')' || *s == ']' || *s == '}') c--;
    cerr << *s++;
  }
  cerr << " = " << x << " , ";
  _DOING(s + 1, tail...);
}
const int INF = 0x3f3f3f3f;
const long long INF64 = 0x3f3f3f3f3f3f3f3fll;
inline int RAND() {
  static int x = 880301;
  return (x = x * 0xdefaced + 1) % 0x7fffffff;
}
const int MAX_N = 2000 + 7;
int A[MAX_N];
int main() {
  int N, x;
  RI(N, x);
  long long ans = 0;
  for (int i = 0; i < int(N); i++) {
    RI(A[i]);
    ans += A[i];
    A[N + i] = A[i];
  }
  for (int i = 1; i <= int(N - 1); i++) {
    long long pans = 1ll * i * x;
    deque<int> deq;
    for (int j = 0; j < int(2 * N); j++) {
      while (!deq.empty() && deq.front() < j - i) deq.pop_front();
      while (!deq.empty() && A[deq.back()] >= A[j]) deq.pop_back();
      deq.push_back(j);
      if (j >= N) pans += A[deq.front()];
    }
    ans = min(ans, pans);
  }
  PL(ans);
  return 0;
}
