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 INF = 1e9 + 7;
const int MOD = 1e9 + 7;
int main() {
  long long N, X;
  long long A[2000];
  long long S = 0;
  vector<long long> V;
  cin >> N >> X;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  vector<long long> U;
  long long i = 0;
  while (A[i] > X) {
    i++;
  }
  long long j = i;
  for (; i < N; i++) {
    U.push_back(A[i]);
  }
  i = 0;
  for (; i < j; i++) {
    U.push_back(A[i]);
  }
  for (int i = 0; i < N; i++) {
    if (X >= U[i]) {
      V.push_back(i);
      S += U[i];
    }
  }
  if ((int)V.size() == N) {
    cout << S << endl;
  } else {
    long long M = V.size();
    V.push_back(N);
    long long MA = 0;
    long long mem;
    for (int i = 0; i < M; i++) {
      if (MA < V[i + 1] - V[i]) {
        MA = V[i + 1] - V[i];
        mem = i;
      }
    }
    cout << (S + X) * (V[mem + 1] - V[mem] - 1) + S << endl;
  }
  return 0;
}
