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;
void reader(int *x) {
  int k, m = 0;
  *x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      *x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    *x = (*x) * 10 + k - '0';
  }
  if (m) (*x) = -(*x);
}
void reader(long long *x) {
  int k, m = 0;
  *x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      *x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    *x = (*x) * 10 + k - '0';
  }
  if (m) (*x) = -(*x);
}
void reader(double *x) { scanf("%lf", x); }
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
template <class T, class S>
void reader(T *x, S *y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T *x, S *y, U *z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T *x, S *y, U *z, V *w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(long long x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(double x, char c) {
  printf("%.15f", x);
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  int i;
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (i = 0; i < n - 1; i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
char memarr[17000000];
void *mem = memarr;
template <class S, class T>
inline void chmin(S &a, T b) {
  if (a > b) a = b;
}
int N, A[2000], X;
int main() {
  int i, j, k;
  long long res = 0;
  reader(&N, &X);
  for (i = 0; i < N; i++) reader(A + i);
  for (k = 0; k < 2; k++) {
    chmin(A[0], A[N - 1] + X);
    for (i = 1; i < N; i++) chmin(A[i], A[i - 1] + X);
  }
  res = accumulate(A, A + N, 0LL);
  writerLn(res);
  return 0;
}
