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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Contest690 {

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

        String s = br.readLine();
        String[] str = s.split(" ");

        int n = Integer.parseInt(str[0]);
        int q = Integer.parseInt(str[1]);
        long k = Integer.parseInt(str[2]);

        s = br.readLine();
        str = s.split(" ");
        long[] arr = new long[n];

        for(int i=0;i<n;i++){
            arr[i] = Integer.parseInt(str[i]);
        }

        long[] pref = new long[n+1];
        long ans = 0;
        if(n>1) {
            ans = arr[1] - arr[0] - 1 + arr[0] - 1;
        }
        else {
            ans = arr[0]-1+k-arr[0];
        }
        pref[1]=ans;
        for (int j = 1; j <n-1 ; j++) {
            ans+=arr[j+1]-arr[j]-1+arr[j]-arr[j-1]-1;
            pref[j+1] = ans;
        }
        if(n>1){
            pref[n]=k-arr[n-1]+arr[n-1]-arr[n-2]-1+ans;
        }

        for (int i = 0; i < q; i++) {
            s = br.readLine();
            str = s.split(" ");
            int li = Integer.parseInt(str[0]);
            int ri = Integer.parseInt(str[1]);
            long cur = 0;
            if(li==ri){
                cur = arr[li-1]-1+k-arr[li-1];
            }
            else if(li+1==ri) {
                cur = arr[li-1]-1+2*(arr[ri-1]-arr[li-1]-1)+k-arr[ri-1];
            }
            else {
                cur = pref[ri-1]-pref[li];
                cur+=arr[li-1]-1+arr[li]-arr[li-1]-1;
                cur+=arr[ri-1]-arr[ri-2]-1+k-arr[ri-1];
            }
            System.out.println(cur);
        }

    }

}

