There are N cities in Republic of AtCoder. The size of the i-th city is A_{i}. Takahashi would like to build N-1 bidirectional roads connecting two cities so that any city can be reached from any other city by using these roads.

Assume that the cost of building a road connecting the i-th city and the j-th city is |i-j| \times D + A_{i} + A_{j}. For Takahashi, find the minimum possible total cost to achieve the objective.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq D \leq 10^9
* 1 \leq A_{i} \leq 10^9
* A_{i} and D are integers.

Input

Input is given from Standard Input in the following format:


N D
A_1 A_2 ... A_N


Output

Print the minimum possible total cost.

Examples

Input

3 1
1 100 1


Output

106


Input

3 1000
1 100 1


Output

2202


Input

6 14
25 171 7 1 17 162


Output

497


Input

12 5
43 94 27 3 69 99 56 25 8 15 46 8


Output

658
#include <algorithm>
#include <cstdio>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <queue>
#include <sstream>
#include <stack>
#include <time.h>
#include <vector>
#include <complex>
#include <map>
#include <set>
#include <iomanip>
#include <math.h>
#include <stdlib.h>
#include <list>
#include <utility>
#include <memory>
#include <cstring>
#include <fstream>
#include <numeric>
#include <assert.h>
#include <bits/stdc++.h>
using namespace std;
#define SIZE 200005
#define INF 10000000000000000LL
typedef long long ll;
typedef pair<int,int> P;
typedef pair<ll,P> PP;
struct UF{
	int par[SIZE],rank[SIZE];
	void init(int n){
		for (int i=0;i<n;i++){
			par[i]=i;
			rank[i]=0;
		}
	}
	int find(int x){
		if (par[x]==x) return x;
		return par[x]=find(par[x]);
	}
	void unite(int x,int y){
		x=find(x);
		y=find(y);
		if (x==y) return;
		if (rank[x]<rank[y]) par[x]=y;
		else{
			par[y]=x;
			if (rank[x]==rank[y]) rank[x]++; 
		}
	}
	bool same(int x,int y){
		return find(x)==find(y);
	}
}uf; 
ll A[SIZE];
ll D;
vector <PP> edge;
void solve(int l,int r){
	if (l==r) return;
	int m=(l+r)/2;
	ll mn=INF;
	int pl=-1;
	for (int i=l;i<=m;i++){
		ll vl=A[i]-D*(ll)i;
		if (mn>vl){
			mn=vl;
			pl=i;
		}
	}
	mn=INF;
	int pr=-1;
	for (int i=m+1;i<=r;i++){
		ll vl=A[i]+D*(ll)i;
		if (mn>vl){
			mn=vl;
			pr=i;
		}
	}
	for (int i=l;i<=m;i++){
		ll vl=A[i]-D*(ll)i;
		ll vr=A[pr]+D*(ll)pr;
		edge.push_back(PP(vl+vr,P(i,pr))); 
	}
	for (int i=m+1;i<=r;i++){
		ll vl=A[pl]-D*(ll)pl;
		ll vr=A[i]+D*(ll)i;
		edge.push_back(PP(vl+vr,P(pl,i))); 
	}
	solve(l,m);
	solve(m+1,r);
}
int main(){
	int n;
	scanf ("%d%lld",&n,&D);
	for (int i=0;i<n;i++) scanf ("%lld",&A[i]);
	solve (0,n-1);
	sort (edge.begin(),edge.end());
	uf.init(n+2);
	ll ret=0;
	for (int i=0;i<edge.size();i++){
		P p=edge[i].second;
		if (!uf.same(p.first,p.second)){
			uf.unite(p.first,p.second);
			ret+=edge[i].first;
		}
	}
	printf("%lld",ret);
	return 0;
}