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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<algorithm>
#include<vector>
#include<numeric>
#include<string>
#include<cmath>
#include<set>
#include<queue>
#include<deque>
#include<bitset>
#include<iomanip>
#include<cctype>
#include<map>

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep2(i,a,b) for (int (i)=a;(i)<(b);(i)++)
#define all(x) (x).begin(),(x).end()

using namespace std;
const int inf = 1001001000;
const long long int Inf = 1001001001001001000;

void print(vector<vector<int>> a){
	for (int i = 0; i < a.size(); i++)
	{
		for (int j=0;j<a[i].size();j++){
			cout << a[i][j] << " ";
		}
		cout << endl;
	}
}

void print(vector<vector<long long int>> a){
	for (int i=0;i<a.size();i++){
		for (int j=0;j<a[i].size();j++){
			cout << a[i][j] << " ";
		}
		cout << endl;
	}
}

void print(vector<int> a){
    int n = a.size();
    for (int j=0;j<n;j++) {
        if (j != n-1) cout << a[j] << " ";
        else cout << a[j] << endl;
    }
}

void print(set<int> a){
	for (auto x:a)
		cout << x << " ";
	cout << endl;
}


int main()
{
	int h, n;
	cin >> h >> n;
	vector<long long int> a(n);
	vector<long long int> b(n);
	rep(i,n){
		cin >> a[i] >> b[i];
	}
	vector<vector<long long int>> dp(n + 1, vector<long long int>(h+1, Inf));
	dp[0][0] = 0;
	rep(i, n) {
		rep(j,h+1){
			if (h-a[i] >= 0)
				dp[i + 1][j] = min(dp[i][j], dp[i + 1][j - a[i]] + b[i]);
			else
				dp[i + 1][j] = dp[i][j];
		}
	}
	cout << dp[n][h] << endl;
	return 0;
}