#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll n,q,k;
vector<ll> a;
vector<ll> p;
ll i,j;
void input()
{
    cin>>i>>j;
}

void solve()
{
    ll ans=0;
    
    for(int ii=0;ii<n;ii++)
    {
        if(ii==0)
        {
            ans+=a[ii+1]-2;
        }
        else if(ii==(n-1))
        {
            ans+=(k-a[ii-1]-1);
        }
        else{
            ans+=(a[ii+1]-a[ii-1]-2);
        }
        p.push_back(ans);
        //cout<<ans<<" ";
    }
   // cout<<endl;
    

}

int main()
{
  cin>>n>>q>>k;
  for(int i=0;i<n;i++)
  {
      ll z;
      cin>>z;
      a.push_back(z);
  }
  solve();
  while(q--)
  {
      ll ans=0;
      input();
      if(i==j) cout<<k-1<<endl;
      else
      {
          ans=(p[j-2]-p[i-1]);
         // cout<<ans<<endl;
          ans+=a[i]-2;
         // cout<<ans<<endl;
          ans+=(k-a[j-2]-1);
         // cout<<ans<<endl;

        cout<<ans<<endl;

      }
      
  }  
    return 0;
}
### Prompt

Generate 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>
using namespace std;
typedef long long int ll;
ll n,q,k;
vector<ll> a;
vector<ll> p;
ll i,j;
void input()
{
    cin>>i>>j;
}

void solve()
{
    ll ans=0;
    
    for(int ii=0;ii<n;ii++)
    {
        if(ii==0)
        {
            ans+=a[ii+1]-2;
        }
        else if(ii==(n-1))
        {
            ans+=(k-a[ii-1]-1);
        }
        else{
            ans+=(a[ii+1]-a[ii-1]-2);
        }
        p.push_back(ans);
        //cout<<ans<<" ";
    }
   // cout<<endl;
    

}

int main()
{
  cin>>n>>q>>k;
  for(int i=0;i<n;i++)
  {
      ll z;
      cin>>z;
      a.push_back(z);
  }
  solve();
  while(q--)
  {
      ll ans=0;
      input();
      if(i==j) cout<<k-1<<endl;
      else
      {
          ans=(p[j-2]-p[i-1]);
         // cout<<ans<<endl;
          ans+=a[i]-2;
         // cout<<ans<<endl;
          ans+=(k-a[j-2]-1);
         // cout<<ans<<endl;

        cout<<ans<<endl;

      }
      
  }  
    return 0;
}
```