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>
#include <boost/multiprecision/cpp_int.hpp>

using namespace boost::multiprecision;

//aが負でも結果を非負にする
int128_t mod(int128_t a, int128_t b) {
	return ((a % b) + b) % b;
}

int main(void) {
	const int128_t INF = 100000000L + 1000000000L * 2000L + 1L;
	int128_t N, x;
	std::vector<int128_t> a;
	int128_t result = 0;
	int128_t num_rot = -1;
	std::cin >> N >> x;
	for(int128_t i = 0; i < N; ++i) {
		int128_t t;
		std::cin >> t;
		a.push_back(t);
	}
	for(int128_t i = 0; i < N; ++i) {
		int128_t minimum = INF;
		int128_t first_index = 0;
		for(int128_t j = 0; j < N; ++j) {
			int128_t t = a[(int)(mod(i - j, N))] + x * j;
			if(t < minimum) {
				minimum = t;
				first_index = j;
			}
		}
		if(num_rot < first_index) {
			num_rot = first_index;
		}
		result += a[(int)(mod(i - first_index, N))];
	}
	result += x * num_rot;
	std::cout << result << '\n';
	return 0;
}

