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 = 2e3 + 10;
int N, X;
int A[MAXN];
int B[MAXN][MAXN];
long long ans = 1ll << 60;
int main() {
  register int i, j;
  scanf("%d%d", &N, &X);
  for (i = 1; i <= N; ++i) scanf("%d", A + i);
  for (i = 1; i <= N; ++i) {
    B[i][0] = A[i];
    for (j = 1; j < N; ++j) {
      int pos = i - j;
      if (pos <= 0) pos = N - abs(pos);
      B[i][j] = min(B[i][j - 1], A[pos]);
    }
  }
  for (j = 0; j < N; ++j) {
    long long res = 0;
    for (i = 1; i <= N; ++i) res += B[i][j];
    ans = min(ans, (long long)res + X * j);
  }
  printf("%lld\n", ans);
  return 0;
}
