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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class keepSorted {
    void run(){
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int q = sc.nextInt();
        int k = sc.nextInt();
        int[] a = sc.readArray(n);
        StringBuilder sb = new StringBuilder();
        while (q-- > 0) {
            int l = sc.nextInt();
            int r = sc.nextInt();
            // count elements not in l to r
            //    index 0 to l, r to maxR
            int elements = r-l;
//                System.out.println(elements);
            int indexSum = a[r-1] - 1 - elements + k - a[l-1] - elements;
//                System.out.println(a[r-1]-elements);
//                System.out.println(k-a[l-1]-elements);
//                System.out.println();
            sb.append(indexSum).append('\n');
        }
        System.out.println(sb);
    }

    public static void main(String[] args) {
        keepSorted solution = new keepSorted();
        solution.run();
    }

    @SuppressWarnings("unused")
    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());
        }
    }
}
