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].
import java.util.*;
import java.awt.image.BandedSampleModel;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Scanner;
public class B {

    static void sort(int[] A){

        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }

    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int n = sc.nextInt();
        int q=sc.nextInt();
        long k=sc.nextLong();
        long arr[] = new long[n+2];
        arr[n+1]=k;
        for(int j=1;j<=n;j++)
        {
            arr[j]=sc.nextLong();
        }

        long dp[]=new long[n+2];
        dp[n+1]=k-1;

        {


            for(int j=1;j<=n;j++)
            {
                long ran=Math.max(arr[j+1]-arr[j-1]-2,0);
//                if(ran==0)
//                {
//                    dp[j]=dp[j-1];
//                }
//                else {
//                    dp[j] = dp[j - 1] * ran;
//                }

                dp[j]=ran;
            }

            //dp[n]=dp[n]+1;
            for(int j=1;j<=n+1;j++)
            {
                dp[j]=dp[j-1]+dp[j];
            }

        }
        StringBuilder ans=new StringBuilder();
        //arr[n+1]=k+1;
        for(int j=0;j<q;j++)
        {
            int x=sc.nextInt();
            int y=sc.nextInt();

            {

                long ff=arr[x-1];
                long fff=k-arr[y+1]+1;

                long fans=(dp[y] - dp[x-1]+ff+fff);
                if(arr[y]==k)
                {
                    fans--;
                }
                ans.append( fans+ "\n");
            }
        }

        System.out.println(ans);

    }
}
