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 (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {
        n:usize,d:i64,a:i64,
        mut xh: [(i64,i64);n],
    }

    xh.sort();
    let x: Vec<i64> = xh.iter().map(|&x| x.0).collect::<Vec<_>>();
    let mut h: Vec<i64> = xh.iter().map(|&x| x.1).collect::<Vec<_>>();

    let mut ans = 0i64;
    let mut r = 0usize;
    let mut t = vec![0; n + 2];
    for left in 0..n {
        if left > 0 {
            t[left] += t[left - 1];
        }
        let mut now = h[left] - t[left];
        if now <= 0 {
            continue;
        }
        let cnt = (now + a - 1) / a;
        ans += cnt;
        let minus = cnt * a;
        // let mut ok = 0;
        // let mut ng = n;
        // while (ng - ok) > 1 {
        //     let mid = (ok + ng) / 2;
        //     if x[mid] <= x[left] + 2 * d {
        //         ok = mid;
        //     } else {
        //         ng = mid;
        //     }
        // }

        r = x.upper_bound(&(x[left] + 2 * d));
        t[left] += minus;
        t[r] -= minus;
        // println!("l={},r={},h: {:?}", left, r, h);
    }
    println!("{}", ans);
}

pub trait BinarySearch<T> {
    fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize;
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound_by<F: Fn(&T) -> bool>(&self, f: F) -> usize {
        let mut ng = -1;
        let mut ok = self.len() as i64;
        while (ok as i32 - ng as i32).abs() > 1 {
            let mid = (ok + ng) / 2;
            if f(&self[mid as usize]) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        ok as usize
    }
    fn lower_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|y| y >= x)
    }
    fn upper_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|y| y > x)
    }
}
static MX: usize = 1010101;
static MOD: i64 = 1000000007;
static INF: i64 = std::i64::MAX >> 1;

pub trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}
pub enum SUM {}
impl Monoid for SUM {
    type T = u64;
    fn id() -> Self::T {
        0
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
}
/// Segment Tree
pub struct SEG<M: Monoid> {
    n: usize,
    buf: Vec<M::T>,
}
impl<M: Monoid> SEG<M> {
    pub fn new(n: usize) -> SEG<M> {
        SEG {
            n,
            buf: vec![M::id(); 2 * n],
        }
    }
    pub fn update(&mut self, k: usize, a: M::T) {
        let mut k = k + self.n;
        self.buf[k] = a;
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    pub fn add(&mut self, k: usize, a: &M::T) {
        let mut k = k + self.n;
        self.buf[k] = M::op(&self.buf[k], a);
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    pub fn get(&self, i: usize) -> M::T {
        self.query(i, i + 1)
    }
    pub fn query_range<R: std::ops::RangeBounds<usize>>(&self, range: R) -> M::T {
        let l = match range.start_bound() {
            std::ops::Bound::Excluded(&x) => {
                assert!(x > 0);
                x - 1
            }
            std::ops::Bound::Included(&x) => x,
            std::ops::Bound::Unbounded => 0,
        };
        let r = match range.end_bound() {
            std::ops::Bound::Excluded(&x) => x,
            std::ops::Bound::Included(&x) => (x + 1),
            std::ops::Bound::Unbounded => self.n,
        };
        self.query(l, r)
    }
    pub fn query(&self, l: usize, r: usize) -> M::T {
        let mut vl = M::id();
        let mut vr = M::id();
        let mut l = l + self.n;
        let mut r = r + self.n;
        while l < r {
            if l & 1 == 1 {
                vl = M::op(&vl, &self.buf[l]);
                l += 1;
            }
            if r & 1 == 1 {
                r -= 1;
                vr = M::op(&self.buf[r], &vr);
            }
            l >>= 1;
            r >>= 1;
        }
        M::op(&vl, &vr)
    }
}