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 <vector>
#include<algorithm>
using namespace std;
long long secNeed(vector<int> &a, int ori, int moveStep,int N,int x){
	int index = ori >= moveStep ? ori - moveStep : ori + N - moveStep;
	return a[index] + moveStep*x;
}
int main()
{	
	int N, x;
	int maxStep = 0;
	cin >> N >> x;
	vector<int> a(N);
	vector<vector<pair<int,int>>> minTime(N);
	for (int i = 0; i < N; ++i){
		cin >> a[i];
	}
	for (int i = 0; i < N; ++i){
		minTime[i].push_back({ i, 0 });
		for (int moveStep = 1; moveStep < N; ++moveStep){
			long long pre = secNeed(a, minTime[i][moveStep - 1].first, minTime[i][moveStep - 1].second, N, x);
			long long cur = secNeed(a, i, moveStep, N, x);
			if (cur < pre){
				minTime[i].push_back({ i, moveStep });
				if (moveStep>maxStep)	maxStep = moveStep;
			}
			else{
				minTime[i].push_back(minTime[i][moveStep - 1]);
			}
		}
	}
	long long minTTTime = 9223372036854775807;
	for (long long i = 0; i <= maxStep; ++i){
		long long sum=0;
		for (int j = 0; j < N; ++j){
			int index = minTime[j][i].first - minTime[j][i].second;
			if (index<0)index += N;
			sum += a[index];
		}
		sum += i*long long(x);
		if (sum < minTTTime)	minTTTime = sum;
	}
	cout << minTTTime << endl;
	return 0;
}