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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Khater
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BReplaceAndKeepSorted solver = new BReplaceAndKeepSorted();
        solver.solve(1, in, out);
        out.close();
    }

    static class BReplaceAndKeepSorted {
        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int t = 1;
            //t = sc.nextInt();
            while (t-- > 0) {
                int n = sc.nextInt();
                int q = sc.nextInt();
                long k = sc.nextInt();
                int[] arr = sc.nextIntArr(n);
                long[] dif = new long[n + 2];
                dif[1] = arr[0] - 1;
                dif[n + 1] = k - arr[n - 1];
                for (int i = 2; i <= n; i++) {
                    dif[i] = arr[i - 1] - arr[i - 2] - 1;
                }
                long[] sum = new long[n + 2];
                sum[0] = dif[0];
                for (int i = 1; i < n + 2; i++) sum[i] = sum[i - 1] + dif[i];
                //	pw.println(Arrays.toString(dif));
                for (int i = 0; i < q; i++) {
                    int l = sc.nextInt();
                    int r = sc.nextInt();
                    long a = k - arr[r - 1];
                    long bet = sum[r] - sum[l];
                    long b = arr[l - 1] - 1;
                    pw.println(a + 2 * bet + b);
                    //	pw.println(a+" "+ bet +" "+ b);
                }
            }

        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

        public int[] nextIntArr(int n) {
            try {
                int[] a = new int[n];
                for (int i = 0; i < n; i++)
                    a[i] = nextInt();
                return a;
            } catch (Exception e) {
                throw new RuntimeException(e);
            }

        }

    }
}

