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
//header{{{
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
#include <ext/pb_ds/trie_policy.hpp>

using namespace __gnu_pbds;
using namespace std;

#define rep(i,n) for(int i=0;i<(n);++i)
#define reps(i,n) for(int i=1;i<=(n);++i)
#define all(x) (x).begin(),(x).end()
#define Fixed fixed << setprecision(12)
#define int int_fast64_t
using pii = pair<int,int>;
constexpr int INF  = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr int mod1 = 1e9+7;
constexpr int mod2 = 998244353;

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class A, class B> inline bool chmax(A &a, const B &b) { return b > a && (a = b, true); }
template <class A, class B> inline bool chmin(A &a, const B &b) { return b < a && (a = b, true); }

template <class T> using min_heap = priority_queue<T,vector<T>,greater<T> >;
template <class T> using max_heap = priority_queue<T>;
template <class A, class B> using umap = unordered_map<A,B>;
template <class T> using Set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <class K, class V> using Umap = gp_hash_table<K, V>;
using Trie = trie<string, null_type, trie_string_access_traits<>, pat_trie_tag, trie_prefix_search_node_update>;

inline int square(int a){ return a * a;}
inline int updiv(int a,int b){ return (a + b - 1) / b; }

constexpr int dx[] = {1,0,-1,0,1,1,-1,-1};
constexpr int dy[] = {0,-1,0,1,1,-1,-1,1};
//}}}


signed main(){
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout.setf(ios_base::fixed);
    cout.precision(10);

    int n, x;
    cin >> n >> x;

    vector<int> a(n);

    rep(i,n){
        cin >> a[i];
    }

    min_heap<pii> pq;
    auto min_cost = a;
    vector<int> pre(n);
    iota(all(pre), 0);
    rep(i,n){
        pq.emplace(a[i], i);
    }
    while(!pq.empty()){
        auto [now_cost, now_node] = pq.top();
        pq.pop();
        if(min_cost[now_node] < now_cost) continue;
        int next_node = (now_node + 1) % n;
        if(chmin(min_cost[next_node], min_cost[now_node] + x)){
            pq.emplace(min_cost[next_node], next_node);
            pre[next_node] = now_node;
        }
    }

    vector<vector<int> > v(n);
    int max_size = 0;
    rep(i,n){
        int now = i;
        v[i].emplace_back(now);
        while(pre[now] != now){
            now = pre[now];
            v[i].emplace_back(now);
        }
        chmax(max_size, v[i].size());
    }

    int res = 0;

    for(int i = max_size - 1; i >= 0; --i){
        bool changed = false;
        rep(j,n){
            if(v[j].size() <= i) continue;
            if(v[j].size() - 1 == i){
                res += a[v[j][i]];
            }else if(!changed){
                res += x;
                changed = true;
            }
        }
    }

    cout << res << '\n';

    return 0;
}