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.*;

public class Main {

    static FastScanner fs = new FastScanner();

    public static void main(String[] args) throws IOException {
        int n=fs.nextInt(), q=fs.nextInt(), k=fs.nextInt();
        int []a=new int[n], b=new int[n];
        for(int i=0;i<n;++i) a[i]=fs.nextInt();
        if(n==1){
            for(int i=0;i<q;++i){
                int l=fs.nextInt(), r=fs.nextInt();
                System.out.println(k-1);
            }
            System.exit(0);
        }
        for(int i=0;i<n;++i){
            if(i==0){
                b[0]=a[1]-2;
            }
            else if(i==n-1){
                b[n-1]=k-a[n-2]-1;
            }
            else{
                b[i]=a[i+1]-a[i-1]-2;
            }
        }
        //for(int i:b) System.out.print(i+" ");
        //System.out.println();
        for(int i=1;i<n;++i) b[i]+=b[i-1];
        //for(int i:b) System.out.print(i+" ");
        //System.out.println();
        for(int i=0;i<q;++i){
            int L=fs.nextInt(), R=fs.nextInt();
            if(L==R){
                System.out.println(k-1);
            }
            else{
                --L; --R;
                int sum=b[R-1]-b[L];
                //System.out.print(sum+" ");
                sum += a[L+1]-2;
                //System.out.print(sum+" ");
                sum += k-a[R-1]-1;
               // System.out.print(sum+"\n");
;               System.out.println(sum);
            }
        }
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}