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>
#pragma GCC optimize("Ofast")
#pragma GCC target("tune=native")
#pragma GCC target("avx")
using namespace std;
const long long mod = 1000000007;
long long n, x, ret;
vector<long long> a;
vector<pair<long long, long long> > operation;
struct SegmentTree {
 private:
  long long n;
  vector<long long> node;

 public:
  SegmentTree(vector<long long> v) {
    long long sz = v.size();
    n = 1;
    while (n < sz) n *= 2;
    node.resize(2 * n - 1, INT_MAX);
    for (long long i = 0; i < (long long)(sz); i++) node[i + n - 1] = v[i];
    for (long long i = (long long)(n - 2) - 1; i >= 0; i--)
      node[i] = min(node[2 * i + 1], node[2 * i + 2]);
  }
  void update(long long k, long long x) {
    k += n - 1;
    node[k] = x;
    while (k) {
      k = (k - 1) / 2;
      node[k] = min(node[2 * k + 1], node[2 * k + 2]);
    }
  }
  long long getmin(long long a, long long b, long long k = 0, long long l = 0,
                   long long r = -1) {
    if (r < 0) r = n;
    if (r <= a || b <= l) return INT_MAX;
    if (a <= l && r <= b) return node[k];
    return min(getmin(a, b, 2 * k + 1, l, (l + r) / 2),
               getmin(a, b, 2 * k + 2, (l + r) / 2, r));
  }
};
signed main() {
  scanf("%lld", &(n));
  scanf("%lld", &(x));
  a.resize(n);
  for (long long i = 0; i < (long long)(n); i++) scanf("%lld", &(a[i]));
  for (long long i = 0; i < (long long)(n); i++) a.push_back((a[i]));
  for (long long i = 0; i < (long long)(n); i++) a.push_back((a[i]));
  SegmentTree st = SegmentTree(a);
  ret = 1145141919810LL;
  for (long long cast = 0; cast < (long long)(n); cast++) {
    long long casttime = cast * x;
    for (long long i = 0; i < (long long)(n); i++)
      casttime += st.getmin(i + n - cast - 1, i + n);
    cerr << casttime << endl;
    ret = min(ret, casttime);
  }
  cout << ret << endl;
}
