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 B{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        static int MOD= 1000000007;
        public void solve(InputReader in, PrintWriter out) {
            int n= in.nextInt(), q= in.nextInt(), k= in.nextInt();
            int[] a= new int[n];
            for(int i=0;i<n;i++) a[i]= in.nextInt();
            long[] presum= new long[n+1];
            presum[1]= n>=2? a[1]-2:k-1;
            presum[1]= Math.max(presum[1],0); 
            for(int i=1;i<n;i++){
                presum[i+1]= presum[i];
                if(i==n-1) presum[i+1]+= Math.max(k-(a[i-1]+1),0);
                else presum[i+1]+= Math.max((a[i+1]-1)-(a[i-1]+1),0);
            }
            // for(long i: presum) out.print(i);
            // out.println();
            while(q-->0){
                int l= in.nextInt()-1, r= in.nextInt()-1;
                if(l==r) out.println(k-1);
                else if(r==l+1){
                    out.println((long)Math.max((long)a[r]-2,0)+Math.max((long)k-(a[l]+1),0));
                }
                else{
                    long res= presum[r-1+1]-presum[l+1];
                    res+= Math.max(a[l+1]-2,0)+ Math.max(k-(a[r-1]+1),0);
                    out.println(res);
                }
            }
            
        }
    }
    static class Pair implements Comparable<Pair>{
        public long x;
        public int y;
        public Pair(long x, int y){
            this.x = x;
            this.y = y;
        }
 
        @Override
        public int compareTo(Pair o) {
            if (this.x > o.x){
                return 1;
            }
            else if (this.x < o.x){
                return -1;
            }
            else{
                return Integer.compare(this.y, o.y);
            }
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;
 
        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }
 
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}
 