Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3 1
1 100 1

Sample Output 1

106

This cost can be achieved by, for example, building roads connecting City 1, 2 and City 1, 3.

Sample Input 2

3 1000
1 100 1

Sample Output 2

2202

Sample Input 3

6 14
25 171 7 1 17 162

Sample Output 3

497

Sample Input 4

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

Sample Output 4

658

Solution in Rust (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules !zero_one_impls {($({$Trait :ident $method :ident $($t :ty ) *,$e :expr } ) *) =>{$($(impl $Trait for $t {#[inline ] fn $method () ->Self {$e } } ) *) *} ;}
zero_one_impls !({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,0 } {Zero zero f32 f64 ,0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 ,1 } {One one f32 f64 ,1. } ) ;
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules !iter_scan_impls {($($t :ty ) *) =>{$(impl IterScan for $t {type Output =Self ;#[inline ] fn scan <'a ,I :Iterator <Item =&'a str >>(iter :&mut I ) ->Option <Self >{iter .next () ?.parse ::<$t >() .ok () } } ) *} ;}
    iter_scan_impls !(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String ) ;
    macro_rules !iter_scan_tuple_impl {($($T :ident ) *) =>{impl <$($T :IterScan ) ,*>IterScan for ($($T ,) *) {type Output =($(<$T as IterScan >::Output ,) *) ;#[inline ] fn scan <'a ,It :Iterator <Item =&'a str >>(_iter :&mut It ) ->Option <Self ::Output >{Some (($(<$T as IterScan >::scan (_iter ) ?,) *) ) } } } ;}
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl !(A B ) ;
    iter_scan_tuple_impl !(A B C ) ;
    iter_scan_tuple_impl !(A B C D ) ;
    iter_scan_tuple_impl !(A B C D E ) ;
    iter_scan_tuple_impl !(A B C D E F ) ;
    iter_scan_tuple_impl !(A B C D E F G ) ;
    iter_scan_tuple_impl !(A B C D E F G H ) ;
    iter_scan_tuple_impl !(A B C D E F G H I ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J ) ;
    iter_scan_tuple_impl !(A B C D E F G H I J K ) ;
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules !min {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::min ($e ,min !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmin {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::min ($dst ,min !($($src ) ,+) ) ;$dst =x ;} } ;}
#[macro_export]
macro_rules !max {($e :expr ) =>{$e } ;($e :expr ,$($es :expr ) ,+) =>{std ::cmp ::max ($e ,max !($($es ) ,+) ) } ;}
#[macro_export]
macro_rules !chmax {($dst :expr ,$($src :expr ) ,+) =>{{let x =std ::cmp ::max ($dst ,max !($($src ) ,+) ) ;$dst =x ;} } ;}
/// binary operaion: $T \circ T \to T$
pub trait Magma {
    /// type of operands: $T$
    type T: Clone + PartialEq;
    /// binary operaion: $\circ$
    fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T;
    #[inline]
    fn reverse_operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
        self.operate(y, x)
    }
}
/// $\forall a,\forall b,\forall c \in T, (a \circ b) \circ c = a \circ (b \circ c)$
pub trait Associative {}
/// associative binary operation
pub trait SemiGroup: Magma + Associative {}
impl<S: Magma + Associative> SemiGroup for S {}
/// $\exists e \in T, \forall a \in T, e \circ a = a \circ e = e$
pub trait Unital: Magma {
    /// identity element: $e$
    fn unit(&self) -> Self::T;
}
/// associative binary operation and an identity element
pub trait Monoid: SemiGroup + Unital {
    /// binary exponentiation: $x^n = x\circ\ddots\circ x$
    fn pow(&self, x: Self::T, n: usize) -> Self::T {
        let mut n = n;
        let mut res = self.unit();
        let mut base = x;
        while n > 0 {
            if n & 1 == 1 {
                res = self.operate(&res, &base);
            }
            base = self.operate(&base, &base);
            n = n >> 1;
        }
        res
    }
}
impl<M: SemiGroup + Unital> Monoid for M {}
/// $\exists e \in T, \forall a \in T, \exists b,c \in T, b \circ a = a \circ c = e$
pub trait Invertible: Magma {
    /// $a$ where $a \circ x = e$
    fn inverse(&self, x: &Self::T) -> Self::T;
    #[inline]
    fn rinv_operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
        self.operate(x, &self.inverse(y))
    }
}
/// associative binary operation and an identity element and inverse elements
pub trait Group: Monoid + Invertible {}
impl<G: Monoid + Invertible> Group for G {}
/// $\forall a,\forall b \in T, a \circ b = b \circ a$
pub trait Commutative {}
/// commutative monoid
pub trait AbelianMonoid: Monoid + Commutative {}
impl<M: Monoid + Commutative> AbelianMonoid for M {}
/// commutative group
pub trait AbelianGroup: Group + Commutative {}
impl<G: Group + Commutative> AbelianGroup for G {}
/// $\forall a \in T, a \circ a = a$
pub trait Idempotent {}
/// idempotent monoid
pub trait IdempotentMonoid: Monoid + Idempotent {}
impl<M: Monoid + Idempotent> IdempotentMonoid for M {}
#[derive(Clone, Debug)]
pub struct SegmentTree<M: Monoid> {
    n: usize,
    seg: Vec<M::T>,
    m: M,
}
impl<M: Monoid> SegmentTree<M> {
    pub fn new(n: usize, m: M) -> Self {
        let n = 1 << format!("{:b}", n - 1).len();
        let seg = vec![m.unit(); 2 * n];
        Self { n, seg, m }
    }
    pub fn from_vec(v: Vec<M::T>, m: M) -> Self {
        let n = 1 << format!("{:b}", v.len() - 1).len();
        let mut seg = vec![m.unit(); 2 * n];
        for (i, x) in v.into_iter().enumerate() {
            seg[n + i] = x;
        }
        for i in (1..n).rev() {
            seg[i] = m.operate(&seg[2 * i], &seg[2 * i + 1]);
        }
        Self { n, seg, m }
    }
    pub fn set(&mut self, k: usize, x: M::T) {
        debug_assert!(k < self.n);
        let mut k = k + self.n;
        self.seg[k] = x;
        k /= 2;
        while k > 0 {
            self.seg[k] = self.m.operate(&self.seg[2 * k], &self.seg[2 * k + 1]);
            k /= 2;
        }
    }
    pub fn update(&mut self, k: usize, x: M::T) {
        debug_assert!(k < self.n);
        let mut k = k + self.n;
        self.seg[k] = self.m.operate(&self.seg[k], &x);
        k /= 2;
        while k > 0 {
            self.seg[k] = self.m.operate(&self.seg[2 * k], &self.seg[2 * k + 1]);
            k /= 2;
        }
    }
    pub fn get(&self, k: usize) -> M::T {
        debug_assert!(k < self.n);
        self.seg[k + self.n].clone()
    }
    pub fn fold(&self, l: usize, r: usize) -> M::T {
        debug_assert!(l < self.n);
        debug_assert!(r <= self.n);
        let mut l = l + self.n;
        let mut r = r + self.n;
        let mut vl = self.m.unit();
        let mut vr = self.m.unit();
        while l < r {
            if l & 1 != 0 {
                vl = self.m.operate(&vl, &self.seg[l]);
                l += 1;
            }
            if r & 1 != 0 {
                r -= 1;
                vr = self.m.operate(&self.seg[r], &vr);
            }
            l /= 2;
            r /= 2;
        }
        self.m.operate(&vl, &vr)
    }
    pub fn fold_all(&self) -> M::T {
        self.seg[1].clone()
    }
    /// left most index [0, r) that satisfies monotonic condition
    pub fn lower_bound_all<F: Fn(&M::T) -> bool>(&self, f: F, r: usize) -> usize {
        if !f(&self.seg[1]) {
            return r;
        }
        let mut acc = self.m.unit();
        let mut pos = 1;
        while pos < self.n {
            pos *= 2;
            let y = self.m.operate(&acc, &self.seg[pos]);
            if !f(&y) {
                acc = y;
                pos += 1;
            }
        }
        std::cmp::min(pos - self.n, r)
    }
    /// left most index [l, r) that satisfies monotonic condition
    pub fn lower_bound<F: Fn(&M::T) -> bool>(&self, f: F, l: usize, r: usize) -> usize {
        let mut acc = self.m.unit();
        let mut pos = l + self.n;
        let mut lim = r + self.n;
        loop {
            let y = self.m.operate(&acc, &self.seg[pos]);
            if f(&y) {
                while pos < self.n {
                    pos *= 2;
                    let y = self.m.operate(&acc, &self.seg[pos]);
                    if !f(&y) {
                        acc = y;
                        pos += 1;
                    }
                }
                return std::cmp::min(pos - self.n, r);
            }
            let is_right = pos & 1 == 1;
            if pos == lim {
                return r;
            }
            pos /= 2;
            lim /= 2;
            if is_right {
                acc = y;
                pos += 1;
            }
        }
    }
    pub fn as_slice(&self) -> &[M::T] {
        &self.seg[self.n..]
    }
}
/// binary operation to select smaller element
#[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
pub struct MinOperation<T: Clone + Ord + MaximumBounded> {
    _marker: std::marker::PhantomData<fn() -> T>,
}
pub trait MaximumBounded {
    fn maximum() -> Self;
}
mod min_operation_impl {
    use super::*;
    macro_rules! impl_maximum_with_max {
        ($t :ty ,$max :expr ) => {
            impl MaximumBounded for $t {
                #[inline]
                fn maximum() -> Self {
                    $max
                }
            }
        };
    }
    impl_maximum_with_max!(usize, std::usize::MAX);
    impl_maximum_with_max!(u8, std::u8::MAX);
    impl_maximum_with_max!(u16, std::u16::MAX);
    impl_maximum_with_max!(u32, std::u32::MAX);
    impl_maximum_with_max!(u64, std::u64::MAX);
    impl_maximum_with_max!(isize, std::isize::MAX);
    impl_maximum_with_max!(i8, std::i8::MAX);
    impl_maximum_with_max!(i16, std::i16::MAX);
    impl_maximum_with_max!(i32, std::i32::MAX);
    impl_maximum_with_max!(i64, std::i64::MAX);
    macro_rules !impl_maximum_tuple {($($T :ident ) *) =>{impl <$($T :MaximumBounded ) ,*>MaximumBounded for ($($T ,) *) {#[inline ] fn maximum () ->Self {($(<$T as MaximumBounded >::maximum () ,) *) } } } ;}
    impl_maximum_tuple!();
    impl_maximum_tuple!(A);
    impl_maximum_tuple !(A B ) ;
    impl_maximum_tuple !(A B C ) ;
    impl_maximum_tuple !(A B C D ) ;
    impl_maximum_tuple !(A B C D E ) ;
    impl_maximum_tuple !(A B C D E F ) ;
    impl_maximum_tuple !(A B C D E F G ) ;
    impl_maximum_tuple !(A B C D E F G H ) ;
    impl_maximum_tuple !(A B C D E F G H I ) ;
    impl_maximum_tuple !(A B C D E F G H I J ) ;
    impl_maximum_tuple !(A B C D E F G H I J K ) ;
    impl<T: Clone + Ord + MaximumBounded> MinOperation<T> {
        pub fn new() -> Self {
            Self {
                _marker: std::marker::PhantomData,
            }
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Magma for MinOperation<T> {
        type T = T;
        #[inline]
        fn operate(&self, x: &Self::T, y: &Self::T) -> Self::T {
            x.min(y).clone()
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Unital for MinOperation<T> {
        #[inline]
        fn unit(&self) -> Self::T {
            MaximumBounded::maximum()
        }
    }
    impl<T: Clone + Ord + MaximumBounded> Associative for MinOperation<T> {}
    impl<T: Clone + Ord + MaximumBounded> Commutative for MinOperation<T> {}
    impl<T: Clone + Ord + MaximumBounded> Idempotent for MinOperation<T> {}
}
#[derive(Clone, Debug)]
pub struct UnionFind {
    parents: Vec<isize>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        let parents = vec![-1; n];
        Self { parents }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if self.parents[x] < 0 {
            x
        } else {
            let xx = self.parents[x] as usize;
            let y = self.find(xx);
            self.parents[x] = y as isize;
            y
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        use std::mem::swap;
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            return false;
        }
        if self.parents[x] > self.parents[y] {
            swap(&mut x, &mut y);
        }
        self.parents[x] += self.parents[y];
        self.parents[y] = x as isize;
        true
    }
    pub fn size(&mut self, x: usize) -> usize {
        let x = self.find(x);
        (-self.parents[x]) as usize
    }
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    pub fn members(&mut self, x: usize) -> Vec<usize> {
        let root = self.find(x);
        (0..self.parents.len())
            .filter(|i| self.find(*i) == root)
            .collect::<Vec<usize>>()
    }
    pub fn roots(&mut self) -> Vec<usize> {
        (0..self.parents.len())
            .filter(|i| self.parents[*i] < 0)
            .collect::<Vec<usize>>()
    }
    pub fn all_group_members(&mut self) -> std::collections::HashMap<usize, Vec<usize>> {
        let mut groups_map = std::collections::HashMap::new();
        for x in 0..self.parents.len() {
            let r = self.find(x);
            groups_map.entry(r).or_insert(vec![]).push(x);
        }
        groups_map
    }
}
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct Adjacent {
    pub id: usize,
    pub to: usize,
}
impl Adjacent {
    pub fn new(id: usize, to: usize) -> Adjacent {
        Adjacent { id, to }
    }
}
#[derive(Clone, Debug, Default)]
pub struct Graph {
    pub vsize: usize,
    pub esize: usize,
    pub graph: Vec<Vec<Adjacent>>,
}
impl Graph {
    pub fn new(vsize: usize) -> Graph {
        Graph {
            vsize,
            esize: 0,
            graph: vec![vec![]; vsize],
        }
    }
    pub fn add_edge(&mut self, from: usize, to: usize) {
        self.graph[from].push(Adjacent::new(self.esize, to));
        self.esize += 1;
    }
    pub fn add_undirected_edge(&mut self, u: usize, v: usize) {
        self.graph[u].push(Adjacent::new(self.esize, v));
        self.graph[v].push(Adjacent::new(self.esize, u));
        self.esize += 1;
    }
    pub fn vertices(&self) -> std::ops::Range<usize> {
        0..self.vsize
    }
    pub fn adjacency(&self, from: usize) -> &Vec<Adjacent> {
        &self.graph[from]
    }
    pub fn eid_cache(&self) -> GraphEidCache<'_> {
        let mut cache = vec![(0, 0); self.esize];
        for u in self.vertices() {
            for a in self.adjacency(u) {
                cache[a.id] = (u, a.to);
            }
        }
        GraphEidCache { graph: self, cache }
    }
}
pub struct GraphScanner<U: IterScan<Output = usize>, T: IterScan> {
    vsize: usize,
    esize: usize,
    directed: bool,
    _marker: std::marker::PhantomData<fn() -> (U, T)>,
}
impl<U: IterScan<Output = usize>, T: IterScan> GraphScanner<U, T> {
    pub fn new(vsize: usize, esize: usize, directed: bool) -> Self {
        Self {
            vsize,
            esize,
            directed,
            _marker: std::marker::PhantomData,
        }
    }
}
impl<U: IterScan<Output = usize>, T: IterScan> MarkedIterScan for GraphScanner<U, T> {
    type Output = (Graph, Vec<<T as IterScan>::Output>);
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
        let mut graph = Graph::new(self.vsize);
        let mut rest = Vec::with_capacity(self.esize);
        for _ in 0..self.esize {
            let (from, to) = (U::scan(iter)?, U::scan(iter)?);
            if self.directed {
                graph.add_edge(from, to);
            } else {
                graph.add_undirected_edge(from, to);
            }
            rest.push(T::scan(iter)?);
        }
        Some((graph, rest))
    }
}
#[derive(Debug, Clone)]
pub struct GraphEidCache<'a> {
    graph: &'a Graph,
    cache: Vec<(usize, usize)>,
}
impl<'a> std::ops::Index<usize> for GraphEidCache<'a> {
    type Output = (usize, usize);
    fn index(&self, index: usize) -> &Self::Output {
        &self.cache[index]
    }
}
impl Graph {
    pub fn minimum_spanning_tree<T: Ord, F: Fn(&usize) -> T>(&self, weight: F) -> Vec<bool> {
        let mut idx: Vec<_> = (0..self.esize).collect();
        idx.sort_by_key(weight);
        let mut uf = UnionFind::new(self.vsize);
        let cache = self.eid_cache();
        let mut res = vec![false; self.esize];
        for eid in idx.into_iter() {
            let (u, v) = cache[eid];
            res[eid] = uf.unite(u, v);
        }
        res
    }
}
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut __in_buf = Vec::new();
    stdin().read_to_end(&mut __in_buf).expect("io error");
    let __in_buf = unsafe { String::from_utf8_unchecked(__in_buf) };
    let mut scanner = Scanner::new(&__in_buf);
    macro_rules !scan {() =>{scan !(usize ) } ;(($($t :tt ) ,*) ) =>{($(scan !($t ) ) ,*) } ;([$t :ty ;$len :expr ] ) =>{scanner .scan_vec ::<$t >($len ) } ;([$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |scan !($t ) ) .collect ::<Vec <_ >>() } ;({$e :expr } ) =>{scanner .mscan ($e ) } ;($t :ty ) =>{scanner .scan ::<$t >() } ;}
    let __out = stdout();
    let mut __out = BufWriter::new(__out.lock());
    macro_rules !print {($($arg :tt ) *) =>(::std ::write !(__out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules !println {($($arg :tt ) *) =>(::std ::writeln !(__out ,$($arg ) *) .expect ("io error" ) ) }
    macro_rules! echo {
        ($iter :expr ) => {
            echo!($iter, '\n')
        };
        ($iter :expr ,$sep :expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let d = scan!();
    let a = scan!([usize; n]);
    let mut g = Graph::new(n);
    let mut cost = Vec::new();
    let mut segl = SegmentTree::new(n, MinOperation::<(usize, usize)>::new());
    let mut segr = SegmentTree::new(n, MinOperation::<(usize, usize)>::new());
    let mut idx: Vec<_> = (0..n).collect();
    idx.sort_by_key(|&i| a[i]);
    for i in idx {
        let j = segl.fold(0, i).1;
        if j != !0 {
            g.add_undirected_edge(i, j);
            cost.push((i - j) * d + a[i] + a[j]);
        }
        let j = segr.fold(i + 1, n).1;
        if j != !0 {
            g.add_undirected_edge(i, j);
            cost.push((j - i) * d + a[i] + a[j]);
        }
        segl.set(i, ((n - i) * d + a[i], i));
        segr.set(i, (i * d + a[i], i));
    }
    let b = g.minimum_spanning_tree(|&i| cost[i]);
    let ans = b
        .into_iter()
        .zip(cost.into_iter())
        .map(|(b, c)| if b { c } else { 0 })
        .sum::<usize>();
    println!("{}", ans);
}