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

int main()
{
    long long int n,q,k,i,j,l,r,s,d = 0;
    cin >> n >> q >> k;
    int ara[100000],arr[100000];
    for(i = 0; i < n; i++)
    {
        cin >> ara[i];
    }
    arr[0] = 0;
    arr[n-1] = 0;
    for(i = 1; i < n-1; i++)
    {
        d += ara[i+1] - ara[i-1] - 2;
        arr[i] = d;
    }
    for(i = 0; i < q; i++)
    {
        s = 0;
        cin >> l >> r;
        if((r-l) == 0)
        {
            s = k-1;
        }
        else if((r-l) >= 1)
        {
            s += ara[l] - 2;
            s += k - ara[r-2]-1;
            if((r-l) >= 2)
            {
                s += arr[r-2] - arr[l-1];
            }
        }
        cout << s << endl;
    }
    return 0;
}

### Prompt

Your challenge is to write 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;

int main()
{
    long long int n,q,k,i,j,l,r,s,d = 0;
    cin >> n >> q >> k;
    int ara[100000],arr[100000];
    for(i = 0; i < n; i++)
    {
        cin >> ara[i];
    }
    arr[0] = 0;
    arr[n-1] = 0;
    for(i = 1; i < n-1; i++)
    {
        d += ara[i+1] - ara[i-1] - 2;
        arr[i] = d;
    }
    for(i = 0; i < q; i++)
    {
        s = 0;
        cin >> l >> r;
        if((r-l) == 0)
        {
            s = k-1;
        }
        else if((r-l) >= 1)
        {
            s += ara[l] - 2;
            s += k - ara[r-2]-1;
            if((r-l) >= 2)
            {
                s += arr[r-2] - arr[l-1];
            }
        }
        cout << s << endl;
    }
    return 0;
}

```