// Problem: B. Replace and Keep Sorted
// Contest: Codeforces - Codeforces Round #701 (Div. 2)
// URL: https://codeforces.com/contest/1485/problem/B
// Memory Limit: 256 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define ll long long
#define mod 1000000007

// templates
#define all(v) v.begin(), v.end()
#define F first
#define S second
#define sz(x) (int)x.size()
#define po(x, y) fixed << setprecision(y) << x
#define ss(s) scanf(" %[^\n]%*c", s)
#define sc(n) scanf("%d", &n)
#define sl(n) scanf("%lld", &n)
#define ps(s) printf("%s\n", s)
#define pr(n) printf("%d\n", n)
#define pl(n) printf("%lld\n", n)
#define prs(n) printf("%d ", n)
#define pls(n) printf("%lld ", n)
using namespace std;

const ll inf = (ll)1e15 + 10;
const int N = (int)1e6 + 10;

void solve() {
  int n, q;
  ll k;
  sc(n), sc(q), sl(k);
  vector<ll> a(n + 2, 0);
  for (int i = 1; i <= n; i++) {
    sl(a[i]);
  }
  a[n + 1] = k;
  vector<ll> pre(n + 2, 0);
  for (int i = 1; i <= n; i++) {
    pre[i] += a[i] - a[i - 1] - 1;
    pre[i] += a[i + 1] - a[i] - 1;
    pre[i] += pre[i - 1];
  }
  while (q--) {
    int l, r;
    sc(l), sc(r);
    if (l == r) {
      pl(k - 1);
      continue;
    }
    if (r - l == 1) {
      ll ans = a[l] - 1 + 2 * (a[r] - a[l] - 1) + k - a[r];
      pl(ans);
      continue;
    }
    ll ans = pre[r - 1] - pre[l];
    ans += a[l] - 1 + (a[l + 1] - a[l] - 1);
    ans += a[r] - a[r - 1] - 1;
    ans += k - a[r];
    pl(ans);
  }
}

int main() {
  // #ifndef ONLINE_JUDGE
  // 	freopen("input.txt", "r", stdin);
  // 	freopen("output.txt", "w", stdout);
  // #endif
  int t = 1;
  // sc(t);
  while (t--) {
    solve();
  }
  //	cerr << (float)clock() / CLOCKS_PER_SEC * 1000 << " ms" << endl;
  return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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
// Problem: B. Replace and Keep Sorted
// Contest: Codeforces - Codeforces Round #701 (Div. 2)
// URL: https://codeforces.com/contest/1485/problem/B
// Memory Limit: 256 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#define ll long long
#define mod 1000000007

// templates
#define all(v) v.begin(), v.end()
#define F first
#define S second
#define sz(x) (int)x.size()
#define po(x, y) fixed << setprecision(y) << x
#define ss(s) scanf(" %[^\n]%*c", s)
#define sc(n) scanf("%d", &n)
#define sl(n) scanf("%lld", &n)
#define ps(s) printf("%s\n", s)
#define pr(n) printf("%d\n", n)
#define pl(n) printf("%lld\n", n)
#define prs(n) printf("%d ", n)
#define pls(n) printf("%lld ", n)
using namespace std;

const ll inf = (ll)1e15 + 10;
const int N = (int)1e6 + 10;

void solve() {
  int n, q;
  ll k;
  sc(n), sc(q), sl(k);
  vector<ll> a(n + 2, 0);
  for (int i = 1; i <= n; i++) {
    sl(a[i]);
  }
  a[n + 1] = k;
  vector<ll> pre(n + 2, 0);
  for (int i = 1; i <= n; i++) {
    pre[i] += a[i] - a[i - 1] - 1;
    pre[i] += a[i + 1] - a[i] - 1;
    pre[i] += pre[i - 1];
  }
  while (q--) {
    int l, r;
    sc(l), sc(r);
    if (l == r) {
      pl(k - 1);
      continue;
    }
    if (r - l == 1) {
      ll ans = a[l] - 1 + 2 * (a[r] - a[l] - 1) + k - a[r];
      pl(ans);
      continue;
    }
    ll ans = pre[r - 1] - pre[l];
    ans += a[l] - 1 + (a[l + 1] - a[l] - 1);
    ans += a[r] - a[r - 1] - 1;
    ans += k - a[r];
    pl(ans);
  }
}

int main() {
  // #ifndef ONLINE_JUDGE
  // 	freopen("input.txt", "r", stdin);
  // 	freopen("output.txt", "w", stdout);
  // #endif
  int t = 1;
  // sc(t);
  while (t--) {
    solve();
  }
  //	cerr << (float)clock() / CLOCKS_PER_SEC * 1000 << " ms" << endl;
  return 0;
}
```