#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

template<typename a, typename b>
ostream& operator<<(ostream& os, const pair<a, b>& pai) {
	os << pai.first << ' ' << pai.second;
	return os;
}
template<typename a, typename b>
istream& operator>>(istream& is, pair<a, b>& pai) {
	is >> pai.first >> pai.second;
	return is;
}

#ifdef ONLINE_JUDGE
#define endl '\n'
#endif

#define INF (INT_MAX / 2)

#define MAX_N 100005

int n, q, k;
int arr[MAX_N];
int psum[MAX_N];

int main() {
	ios_base::sync_with_stdio(false); std::cin.tie(NULL);
	
	cin >> n >> q >> k;
	for (int i = 1; i <= n; ++i)
		cin >> arr[i];

	while (q--) {
		int l, r;
		cin >> l >> r;
		cout << (k + 1 + arr[r] - arr[l] - (r - l + 1) * 2) << endl;
	}

	return 0;
}
### Prompt

Please create a solution in cpp to the following problem:

Given a positive integer k, two arrays are called k-similar if:

  * they are strictly increasing; 
  * they have the same length; 
  * all their elements are positive integers between 1 and k (inclusive); 
  * they differ in exactly one position. 



You are given an integer k, a strictly increasing array a and q queries. For each query, you are given two integers l_i ≤ r_i. Your task is to find how many arrays b exist, such that b is k-similar to array [a_{l_i},a_{l_i+1}…,a_{r_i}]. 

Input

The first line contains three integers n, q and k (1≤ n, q ≤ 10^5, n≤ k ≤ 10^9) — the length of array a, the number of queries and number k.

The second line contains n integers a_1, a_2, …,a_n (1 ≤ a_i ≤ k). This array is strictly increasing — a_1 < a_2 < … < a_n.

Each of the following q lines contains two integers l_i, r_i (1 ≤ l_i ≤ r_i ≤ n).

Output

Print q lines. The i-th of them should contain the answer to the i-th query.

Examples

Input


4 2 5
1 2 4 5
2 3
3 4


Output


4
3


Input


6 5 10
2 4 6 7 8 9
1 4
1 2
3 5
1 6
5 5


Output


8
9
7
6
9

Note

In the first example:

In the first query there are 4 arrays that are 5-similar to [2,4]: [1,4],[3,4],[2,3],[2,5].

In the second query there are 3 arrays that are 5-similar to [4,5]: [1,5],[2,5],[3,5].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

template<typename a, typename b>
ostream& operator<<(ostream& os, const pair<a, b>& pai) {
	os << pai.first << ' ' << pai.second;
	return os;
}
template<typename a, typename b>
istream& operator>>(istream& is, pair<a, b>& pai) {
	is >> pai.first >> pai.second;
	return is;
}

#ifdef ONLINE_JUDGE
#define endl '\n'
#endif

#define INF (INT_MAX / 2)

#define MAX_N 100005

int n, q, k;
int arr[MAX_N];
int psum[MAX_N];

int main() {
	ios_base::sync_with_stdio(false); std::cin.tie(NULL);
	
	cin >> n >> q >> k;
	for (int i = 1; i <= n; ++i)
		cin >> arr[i];

	while (q--) {
		int l, r;
		cin >> l >> r;
		cout << (k + 1 + arr[r] - arr[l] - (r - l + 1) * 2) << endl;
	}

	return 0;
}
```