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 Python (3.4.3) (judge verdict: Runtime Error)

from bisect import bisect_right
def getVal(i):  # get value of node (i,i)
    v = T[(i,i)][0]
    cur = (i,i)
    cur = T[cur][1]
    while cur[0]>=0:
        v += T[cur][0]
        cur = T[cur][1]
    return v
def udT(i,j,x,node):  # add x between [i,j] where current node is given
    l,r = node[0],node[1]
    if i<=l and r<=j:
        T[node][0] += x
    elif i>r or j<l:
        return
    else:
        udT(i,j,x,T[node][2])
        udT(i,j,x,T[node][3])
N,D,A = map(int,input().split())
X = sorted([list(map(int,input().split())) for _ in range(N)],key=lambda x:x[0])
n = 0
m = N
while m>0:
    m = m//2
    n += 1
if N==2**(n-1):
    n -= 1
for i in range(N,2**n):  # fill in the remainder of N
    X.append([X[-1][0]+1,0])
# Construction of Tree
Y = [X[i][0] for i in range(N)]  # Tree structure
T = {(i,i):[X[i][1],(i,i+1) if i%2==0 else (i-1,i),(-1,-1),(-1,-1)] for i in range(2**n)}  # T[node] = [value,parent,left_child,right_child]
for h in range(n):
    for i in range(2**h):
        d = 2**(n-h)  # interval length of each node
        if h==0:
            T[(i*d,(i+1)*d-1)] = [0,(-1,-1),(i*d,i*d+d//2-1),((i+1)*d-d//2,(i+1)*d-1)]
        else:
            T[(i*d,(i+1)*d-1)] = [0,(i*d,i*d+2*d-1) if (i*d)%2**(n-h+1)==0 else ((i+1)*d-2*d,(i+1)*d-1),(i*d,i*d+d//2-1),((i+1)*d-d//2,(i+1)*d-1)]
cnt = 0
cur = 0
while cur<N:
    x = Y[cur]
    v = getVal(cur)
    if v%A==0:
        k = v//A
    else:
        k = v//A+1
    ind = bisect_right(Y,x+2*D)
    udT(cur,ind-1,-k*A,(0,2**n-1))
    cnt += k
    flag = 0
    for i in range(cur+1,N):
        if getVal(i)>0:
            cur = i
            flag = 1
            break
    if flag==0:
        cur = N
print(cnt)