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].
//package Codeforces;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Round701Div2_2 {


    public static void main(String[] args) throws IOException {
        BufferedReader br= new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st= new StringTokenizer(br.readLine());
        int n= Integer.parseInt(st.nextToken());
        int q= Integer.parseInt(st.nextToken());
        int k= Integer.parseInt(st.nextToken());

        st= new StringTokenizer(br.readLine());
        int a[]= new int[n];
        for (int i=0;i<a.length;i++){
            a[i]= Integer.parseInt(st.nextToken());
        }


        if (n==1){
            while (q-->0){
                System.out.println(k-1);
            }
        }else {
            int temp[]= new int[n];
        temp[0]=a[1]-1-1;
        for (int i=1;i<n-1;i++){
            temp[i]=a[i+1]-a[i-1]-2;
        }

        temp[n-1]=k-a[n-2]-1;

        for (int i=1;i<=n-1;i++){
            temp[i]=temp[i]+temp[i-1];
        }
        while (q-->0) {
            st = new StringTokenizer(br.readLine());
            int l = Integer.parseInt(st.nextToken());
            int r = Integer.parseInt(st.nextToken());

            l--;
            r--;
            int ans = 0;
            if (l == r) {
                ans = k - 1;
            } else {
                ans += (k - a[r - 1] - 1);
                ans += (a[l + 1] - 1 - 1);

                l++;
                r--;

                if (r >= l) {
                    ans += (temp[r] - temp[l - 1]);
                }


            }

            System.out.println(ans);
        }
        }
    }
}
