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 com.company;

import java.util.Scanner;

public class Codeforces {
    // 2 4 6 7 8 9
    // 2 4 6 7 => 1 4 6 7, 2 3 6 7, 2
    // {1,3} {3,5} 5 8,9,10

    // 2 4
    // {1,3} {5..10}

    // 6 7 8
    //{1..5} 0 {9,10}
    private static void sport(int[] a, int[][] q, int k) {
        if (a.length == 1) {
            for (int i = 0; i < q.length; i++) {
                System.out.println(k-1);
            }
            return;
        }
        //930343233
        //930343232
        int n = a.length;
        long[] p = new long[n + 1];
        p[1] = a[1] - 2;
        for (int i = 1; i < n - 1; i++) {
            p[i + 1] =(long) (p[i] + a[i + 1] - a[i - 1] + 1 - 3);
        }
        p[n] = p[n - 1] + Math.max(0, k - a[n - 2] - 1);
        for (int[] ints : q) {
            int l = ints[0] - 1;
            int r = ints[1] - 1;
            if (r==l){
                System.out.println(k-1);
                continue;
            }
            if (r==0){
                System.out.println(a[1]-2);
            }else if (l==n-1){
                System.out.println(k - a[l - 1] - 1);
            }else {
                System.out.println(a[l + 1] - 2 + p[r] - p[l + 1] + Math.max(0, k - a[r - 1] - 1));
            }
        }
    }

    //1 2 4 5
    //2 4
    //{1,3} {5}

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int q = sc.nextInt();
        int k = sc.nextInt();
        int[] a = new int[n];
        int[][] r = new int[q][2];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        for (int i = 0; i < q; i++) {
            r[i] = new int[] {sc.nextInt(), sc.nextInt()};
        }
        sport(a, r, k);
    }
}