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;
struct light {
  int v, k, c, l;
} num[1010];
int s[1100];
bool cmp(light a, light b) { return a.v < b.v; }
int d[1100];
int main() {
  int n;
  while (cin >> n && n != 0) {
    memset(d, 0, sizeof(d));
    int i;
    for (i = 1; i <= n; i++)
      cin >> num[i].v >> num[i].k >> num[i].c >> num[i].l;
    sort(num + 1, num + n + 1, cmp);
    for (i = 1; i <= n; i++) s[i] = s[i - 1] + num[i].l;
    int j;
    for (i = 1; i <= n; i++) {
      d[i] = 0x3f3f3f;
      for (j = 0; j < i; j++) {
        d[i] = min(d[i], d[j] + (s[i] - s[j]) * num[i].c + num[i].k);
      }
    }
    cout << d[n] << endl;
  }
  return 0;
}
