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 <iostream>
#include <cstdint>
#include <vector>
#include <algoirhtm>

using namespace std;

int main()
{
int64_t N, x;
cin >> N >> x;
vector<int64_t> times(N);
for (int64_t &t : times) cin >> t;

int64_t best=N*(int64_t)2000000000;

int64_t dx = 0;
for (int i=0 ; i<N ; i++, dx+=x)
{
int64_t sum=0;
for (int j=0 ; j<N ; j++)
{
sum += times[j];
times[j] = min(times[j], times[(j+N-1)%N]);
} // for j
best = min(best, sum+dx);
} // for i

cout << best << "\n";
} // main
