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.InputStreamReader;
import java.io.InputStream;

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

    static class BZamenaIVozrastanie {
        InputReader in;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.in = in;

            int n = ni();
            int q = ni();
            int k = ni();
            long[] a = nla(n);
            long[] b = new long[n];
            for (int i = 0; i < n; i++) {
                if (i == 0) {
                    if (i == n - 1) {
                        b[i] = k - 1;
                    } else {
                        b[i] = Math.max(0, a[i + 1] - 2);
                    }
                } else if (i == n - 1) {
                    b[i] = Math.max(0, k - a[i - 1] - 1);
                } else {
                    b[i] = Math.max(0, a[i + 1] - a[i - 1] - 2);
                }

                if (i > 0) b[i] += b[i - 1];
            }

            while (q-- > 0) {
                int l = ni() - 1;
                int r = ni() - 1;

                if (l == r) {
                    out.println(k - 1);
                    continue;
                }

                long res = b[r - 1] - b[l];

                res += Math.max(0, a[l + 1] - 2);
                res += Math.max(0, k - a[r - 1] - 1);

                out.println(res);
            }
        }

        private long[] nla(int size) {
            return in.nextLongArray(size);
        }

        private int ni() {
            return in.nextInt();
        }

    }

    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public long[] nextLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextLong();
            }
            return array;
        }

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

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

    }
}

