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.util.*;
import java.io.*;

public class B_ps {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        int q = sc.nextInt();
        int k = sc.nextInt();
        int[] arr = sc.readArray(n);
        int[] presum = new int[n+1];
        precalc(presum, arr, n, k);
        while(q-- != 0) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            if(b-a < 1) {
                out.println(k-1);
                continue;
            }
            a--;
            int ans = arr[a+1] - 2;
            ans +=  k - arr[b-2] - 1;
            ans += presum[b-1] - presum[a+1];
            out.println(ans);
        }

        out.close();
    }

    static void precalc(int[] presum, int[] arr, int n, int k) {
        for(int i=1; i<n-1; i++) {
            presum[i+1] = presum[i] + arr[i+1] - arr[i-1] - 2;
        }
    }

    static int solve(int[] arr, int n) { 

        return 0;
    }

    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();
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return null;
        }

        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());
        }
    }

}