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 long long N = 2e4 + 20;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = (x << 3) + (x << 1) + (ch & 15);
    ch = getchar();
  }
  return x * f;
}
long long n, x, ans = 0x7fffffff, k;
long long a[N], b[N], f[N];
inline long long dp(long long k) {
  memset(f, 0, sizeof(f));
  memset(a, 0, sizeof(a));
  for (long long i = k; i < k + n; i++) a[i - k + 1] = b[i % n];
  for (long long i = 1; i <= n; i++) f[i] = f[i - 1] + a[i];
  for (long long i = 1; i <= n; i++) f[i] = min(f[i], f[i - 1] + x + a[1]);
  return f[n];
}
int main() {
  n = read(), x = read();
  for (long long i = 0; i < n; i++) b[i] = read();
  for (long long i = 0; i < n; i++) ans = min(ans, dp(i));
  printf("%lld\n", ans);
  return 0;
}
