Problem:
Score : 600 points

Problem Statement

Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq D \leq 10^9

1 \leq A \leq 10^9

0 \leq X_i \leq 10^9

1 \leq H_i \leq 10^9

X_i are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N D A
X_1 H_1
:
X_N H_N

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case,unused_imports)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BinaryHeap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut buf_it = buf.split_whitespace();

    let N = buf_it.next().unwrap().parse::<usize>().unwrap();
    let D = buf_it.next().unwrap().parse::<isize>().unwrap();
    let A = buf_it.next().unwrap().parse::<isize>().unwrap();
    let mut XH = (0..N)
        .map(|_| (buf_it.next().unwrap().parse::<isize>().unwrap(),
                    buf_it.next().unwrap().parse::<isize>().unwrap())).collect::<Vec<_>>();
    XH.push((-1000000000 as isize,0));
    XH.sort();

    for i in 0..N+1{
        let h = XH[i].1;
        XH[i].1 = (h-1)/A + 1;
    }

    let mut ans = 0;
    let mut bomb = SegmentTree::<isize>::new(N+1,add,0);

    for i in 1..N+1{
        let (x,h) = XH[i];
        let mut j;
        let mut l = 0;
        let mut r = i;
        while l+1<r {
            j = (l+r)/2;
            if XH[j].0 < x-2*D{
                l = j;
            } else {
                r = j;
            }
        }
        j = r;
        let m = bomb.get(j,i);
        let n = max(0,h-m);
        ans += n;
        bomb.set(i,n);
    }
    println!("{}",ans);

}

fn add(x:isize,y:isize) -> isize{
    x+y
}

struct SegmentTree<N>{
    n: usize,
    T: Vec<N>,
    func: fn(N,N) -> N,
    identity: N,
}

impl<N:Copy> SegmentTree<N> {
    fn new(n:usize,func:fn(N,N) -> N,identity:N) -> SegmentTree<N>{
        let mut T = SegmentTree { n:n,T:Vec::new(),func:func,identity:identity};
        T.init();
        T
    }
    fn init(&mut self){
        self.n = 1<<format!("{:b}",self.n-1).len();
        self.T = (0..(2*self.n-1)).map(|_| self.identity).collect();
    }
    fn set(&mut self,index:usize,value:N){
        let i = index + self.n - 1;
        self.T[i] = value;
        self._update_parent((i-1)/2);
    }
    fn _update_parent(&mut self,i:usize){
        self.T[i] = (self.func)(self.T[i*2+1],self.T[i*2+2]);
        if i>0 { self._update_parent((i-1)/2)}
    }
    fn get(&self,l:usize,r:usize) -> N{
    self._get(l,r,0,0,self.n)
    }
    fn _get(&self,l:usize,r:usize,i:usize,a:usize,b:usize) -> N{
        if l<=a && b<=r {
            self.T[i]
        } else if b<=l || r<=a {
            self.identity
        } else{
            (self.func)(self._get(l,r,2*i+1,a,(a+b)/2),
                        self._get(l,r,2*i+2,(a+b)/2,b))
        }
    }
}