I want u to act as an IOI gold Medalist, u should think very hard about this problem, and solve it using this template
#include <bits/stdc++.h>
#define int long long
using namespace std;

signed main()
{
cin.tie(0);
ios_base::sync_with_stdio(false);
///

}


there should be no comments in the code, but u will explain ur code and heuristics and intuition on how u think of it, and tricks on to use for other problems, all in a nic format that doesnt look bad and weird lol

here is the problem:


JOI-kun is breeding N fish in a large tank, and each fish is numbered from 1 to N.
JOI-kun has two types of fish food, A and B, both in sufficient quantities. When one piece of food is added to
the aquarium, exactly one fish eats it (any fish could potentially eat it), and depending on the type of food and
which fish ate it, the intelligence of the fish changes as follows:
• When fish k (1 ≤ k ≤ N) eats one piece of type A food, the intelligence of fish k increases exactly by D.
• When fish k (1 ≤ k ≤ N) eats one piece of type B food, the intelligence of all fish numbered k and above
increases exactly by 1 each.
Currently, the intelligence of all fish is 0. JOI-kun wants to make the intelligence of fish i (1 ≤ i ≤ N) equal
to its ideal intelligence Ci
, but it may not always be possible.
Therefore, he considered Q questions. The j-th question (1 ≤ j ≤ Q) is as follows:
• Starting from the state where all fish have an intelligence of 0, by repeating the action of putting food
into the aquarium zero or more times, is it possible to reach the state where all fish Lj
, Lj + 1, . . . , Rj
have their exact ideal intelligence values? Furthermore, if it is possible, what is the minimum number of
pieces of type A food that needs to be put into the tank?
Write a program that, given information about JOI-kun’s fish and information about the questions, answers
his questions.

input
N D
C_1 C_2 ... C_N
Q
L_1 R_1
L_2 R_2
.
.
.
L_Q R_Q

Output
Write Q lines to the standard input. In the j-th line (1 ≤ j ≤ Q), if it is possible to reach the state where all
fish Lj
, Lj + 1, . . . , Rj have their exact ideal intelligence values, output the minimum number of pieces of type
A food that needs to be put into the tank. Otherwise, output -1.
Constraints
• 1 ≤ N ≤ 300 000.
• 1 ≤ Q ≤ 300 000.
• 1 ≤ D ≤ 1012
.
• 0 ≤ Ci ≤ 1012 (1 ≤ i ≤ N).
• 1 ≤ Lj ≤ Rj ≤ N (1 ≤ j ≤ Q).
• Given values are all integers.
Subtasks
1. (9 points) N ≤ 3 000, Q ≤ 3 000.
2. (7 points) Ci ≤ 1 (1 ≤ i ≤ N).
3. (28 points) D = 1.
4. (20 points) Ci ≥ Ci+1 (1 ≤ i ≤ N − 1).
5. (36 points) No additional constraints

SAMPLE INPUT AND OUTPUT
sample input 1
4 2
3 1 2 1
1
1 3
sample output 1:
1

For example, in the following case, all fish 1, 2, 3 eventually have their exact ideal intelligence values, and
the number of pieces of type A food put into the tank is 1.
• At first, the intelligence of fish 1, 2, 3, 4 is 0, 0, 0, 0 respectively.
• Next, JOI-kun puts one piece of type B food into the tank, which fish 3 eats. As a result, the intelligence
of fish 1, 2, 3, 4 becomes 0, 0, 1, 1 respectively.
• Next, JOI-kun puts one piece of type A food into the tank, which fish 1 eats. As a result, the intelligence
of fish 1, 2, 3, 4 becomes 2, 0, 1, 1 respectively.
• Finally, JOI-kun puts one piece of type B food into the tank, which fish 1 eats. As a result, the intelligence
of fish 1, 2, 3, 4 becomes 3, 1, 2, 2 respectively

Since it is impossible to reach the state where all fish 1, 2, 3 have the exact ideal intelligence values without
putting any piece of type A food, output 1.
This sample input satisfies the constraints of Subtasks 1, 5.

sample input 2
4 2
0 1 0 1
3
1 2
2 3
1 1

sample output2
0
-1
0

sample input 3
5 1
3 1 4 1 5
3
1 5
2 4
3 5

sample output 3
5
3
3

sample input 4
6 3
16 14 13 8 6 5
4
1 4
2 5
3 3
1 6

sample output 4
9
8
0
-1


MAKE SURE THE SAMPLE TESTCASES R CORRECT FOR UR CODE!!!! U HAVE TO THINK HARD OK, AND TO VERIFY WITH PROOF, THINK MATHEMATICALLY U NEED TO USE DYNAMIC PROGRAMMING