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)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

#[allow(dead_code)]
struct Scanner<'a> {
    cin: StdinLock<'a>,
}
#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read<T: FromStr>(&mut self) -> Option<T> {
        let token = self
            .cin
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn input<T: FromStr>(&mut self) -> T {
        self.read().unwrap()
    }

    fn vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
        (0..len).map(|_| self.input()).collect()
    }

    fn mat<T: FromStr>(&mut self, row: usize, col: usize) -> Vec<Vec<T>> {
        (0..row).map(|_| self.vec(col)).collect()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n: usize = sc.input();
    let d: i64 = sc.input();
    let a: i64 = sc.input();
    let mut arr: Vec<(i64, i64)> = (0..n).map(|_| (sc.input(), sc.input())).collect();

    arr.sort();

    let mut ans: i64 = 0;
    let mut bit = Bit::new(n + 1);

    for i in 0..n {
        let (x, mut h) = arr[i].clone();
        h -= bit.sum(i);

        if h <= 0 {
            continue;
        }

        let num = (h + a - 1) / a;
        ans += num;
        let damage = num * a;
        bit.add(i, damage);
        let rx = x + d * 2;

        let mut ok = 0;
        let mut ng = n as i64;
        while (ok - ng).abs() > 1 {
            let mid = (ok + ng) / 2;
            if arr[mid as usize].0 <= rx {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        bit.add(ng as usize, -damage);
    }

    println!("{}", ans);
}

struct Bit {
    // Binary Indexed Tree
    n: usize,
    data: Vec<i64>,
}

impl Bit {
    fn new(n: usize) -> Bit {
        let mut m = 1;
        while m < n {
            m *= 2;
        }
        Bit {
            n: n,
            data: vec![0; m],
        }
    }

    fn sum(&self, i: usize) -> i64 {
        let mut i = i + 1;
        let mut ret = 0;
        while i > 0 {
            ret += self.data[i - 1];
            i -= (i as i64 & -(i as i64)) as usize;
        }
        ret
    }

    fn add(&mut self, i: usize, x: i64) {
        let mut i = i + 1;
        while i < self.n {
            self.data[i - 1] += x;
            i += (i as i64 & -(i as i64)) as usize;
        }
    }
}