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.io.*;
import java.util.*;
import java.math.*;
//@SuppressWarnings("unused")

public class Solution {

    private static void one() throws Exception {
        rl();
            int n  = nin();
            int q = nin();
            int k = nin();

        int[] a = new int[n+1];
        rl();
        for(int i = 1;i<=n;i++) {a[i] = nin(); }
        while(q-->0){
            int count = 0;
            rl();
            int l = nin(), r = nin();
            count+= a[l]-1;
            count+=k-a[r];
            count += 2*((a[r]-a[l] + 1) - (r-l+1));
            System.out.println(count);
        }

    }

    public static void main(String[] args) throws Exception{
        br = new BufferedReader(new InputStreamReader(System.in));
        bw = new BufferedWriter(new OutputStreamWriter(System.out));

  /*      rl();
        int t = nin() ;
        for(int i =0 ;i<t;i++) {
            one();
        }
        bw.flush();*/
one();
    }

    //helper methods and classes
    static BufferedReader br;
    static BufferedWriter bw;
    static StringTokenizer st;

    static void rl() throws Exception{
        st = new StringTokenizer(br.readLine());
    }
    static long nlo(){
        return Long.parseLong(st.nextToken());
    }
    static int nin(){
        return Integer.parseInt(st.nextToken());
    }
    /*private static void te(){
      }*/
    static double ndo(){
        return Double.parseDouble(st.nextToken());
    }
    static char[] nca(){
        return st.nextToken().toCharArray();
    }


    //helper class
    static class Pair<T,K>{
        T first;
        K second;
        Pair(T first,K second) {
            this.first = first;
            this.second = second;
        }

        public Pair() {

        }
    }
}
