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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
)

var sc *bufio.Scanner
var out *bufio.Writer

func main() {
	sc = bufio.NewScanner(os.Stdin)
	out = bufio.NewWriter(os.Stdout)
	buf := make([]byte, 1<<20)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)
	defer out.Flush()

	n, d, a := nextInt(), nextInt(), nextInt()

	t := newTree(n)
	xi := make([]int, n)
	xpos := make(map[int]int, n)
	for i := 0; i < n; i++ {
		x, h := nextInt(), nextInt()
		xi[i] = x
		xpos[x] = i
		t.set(i, h)
	}
	sort.Sort(sort.IntSlice(xi))
	t.build()

	result := 0
	for _, x := range xi {
		i := xpos[x]
		if t.query(i, i+1) == 0 {
			continue
		}
		r := binSearch(xi[i:], x+2*d) + i + 1
		atkCnt := int(math.Ceil(float64(t.query(i, i+1)) / float64(a)))
		t.update(i, r, -a*atkCnt)
		result += atkCnt
		if t.query(0, t.size) == 0 {
			break
		}
	}

	fmt.Fprintln(out, result)
}
func intMax(a, b int) int {
	if a > b {
		return a
	}
	return b
}
func binSearch(arr []int, target int) int {
	l, r := 0, len(arr)
	for l < r-1 {
		mid := l + (r-l)/2
		if target < arr[mid] {
			r = mid
		} else {
			l = mid
		}
	}
	return l
}

type tree struct {
	node, lazy []int
	size       int
	ex, em     int
}

func newTree(n int) *tree {
	size := 1
	for size < n {
		size <<= 1
	}
	return &tree{
		node: make([]int, 2*size-1),
		lazy: make([]int, 2*size-1),
		size: size,
		ex:   0,
		em:   0,
	}
}
func (t *tree) set(i, v int) {
	t.node[i+t.size-1] = v
}
func (t *tree) build() {
	for k := t.size - 2; k >= 0; k-- {
		t.node[k] = intMax(t.node[2*k+1], t.node[2*k+2])
	}
}
func (t *tree) eval(k, len int) {
	if t.lazy[k] != t.em {
		if k < t.size-1 {
			t.lazy[2*k+1] += t.lazy[k]
			t.lazy[2*k+2] += t.lazy[k]
		}
		t.node[k] = intMax(0, t.node[k]+t.lazy[k]*len)
		t.lazy[k] = t.em
	}
}
func (t *tree) update(a, b, v int) {
	t.ureq(a, b, v, 0, 0, t.size)
}
func (t *tree) ureq(a, b, v, k, l, r int) {
	t.eval(k, b-a)
	if b <= l || r <= a {
		return
	}
	if a <= l && r <= b {
		t.lazy[k] = v
		t.eval(k, b-a)
	} else {
		t.ureq(a, b, v, 2*k+1, l, (l+r)/2)
		t.ureq(a, b, v, 2*k+2, (l+r)/2, r)
		t.node[k] = intMax(0, t.node[2*k+1]+t.node[2*k+2])
	}
}
func (t *tree) query(a, b int) int {
	return t.qreq(a, b, 0, 0, t.size)
}
func (t *tree) qreq(a, b, k, l, r int) int {
	if b <= l || r <= a {
		return t.ex
	}
	t.eval(k, b-a)
	if a <= l && r <= b {
		return t.node[k]
	}
	vl := t.qreq(a, b, 2*k+1, l, (l+r)/2)
	vr := t.qreq(a, b, 2*k+2, (l+r)/2, r)
	return vl + vr
}

func next() string {
	sc.Scan()
	return sc.Text()
}
func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}