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
int main(){
	int N, x;
	cin >> N >> x;
	vector<int> a(N);
	for (int i = 0; i < N; ++i){
		cin >> a[i];
	}

	vector<int> minA = a;
	long long minTTTime = 9223372036854775807;
	for (int ms = 0; ms < N; ++ms){
		for (int i = 0; i<N; ++i){
			int mIndex = i - ms;
			if (mIndex<0)	mIndex += N;
			if (minA[i]>a[mIndex])	minA[i] = a[mIndex];
		}
		long long sum = 0;
		for (auto &el : minA){
			sum += (long long)el;
		}
		sum += (long long)ms*x;
		if (sum < minTTTime)	minTTTime = sum;
	}
	cout << minTTTime << endl;
	cin >> N;

}
