#include <bits/stdc++.h>
typedef long long ll;
typedef long double ld;
using namespace std;
#define F first
#define S second
#define pb push_back  
#define all(x) (x).begin(), (x).end()
#define SZ(x) (int)(x).size()
#define int ll
 
const int N = 1e5 + 10;
int a[N], pref[N];

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0); 
  cout.tie(0);
  int n, q, k;
  cin >> n >> q >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = 2; i < n; i++) {
    pref[i] = pref[i - 1] + (a[i + 1] - a[i - 1] - 2);
  }
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    if (l == r) {
      cout << k - 1 << '\n';
      continue;
    }
    int cnt = pref[r - 1] - pref[l];
    //cerr << "KEK " << cnt << '\n';
    cnt += a[l + 1] - 2;
    cnt += (k - a[r - 1] - 1);
    cout << cnt << '\n';
  }
}     
### Prompt

Your task is to create a Cpp solution 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>
typedef long long ll;
typedef long double ld;
using namespace std;
#define F first
#define S second
#define pb push_back  
#define all(x) (x).begin(), (x).end()
#define SZ(x) (int)(x).size()
#define int ll
 
const int N = 1e5 + 10;
int a[N], pref[N];

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0); 
  cout.tie(0);
  int n, q, k;
  cin >> n >> q >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = 2; i < n; i++) {
    pref[i] = pref[i - 1] + (a[i + 1] - a[i - 1] - 2);
  }
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    if (l == r) {
      cout << k - 1 << '\n';
      continue;
    }
    int cnt = pref[r - 1] - pref[l];
    //cerr << "KEK " << cnt << '\n';
    cnt += a[l + 1] - 2;
    cnt += (k - a[r - 1] - 1);
    cout << cnt << '\n';
  }
}     
```