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 Main {
	static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
	public static void main(String[] args) throws Exception {
		String [] s1 = in.readLine().trim().split(" ");
		String [] s2 = in.readLine().trim().split(" ");
		int n = Integer.parseInt(s1[0]);
		int q = Integer.parseInt(s1[1]);
		int k = Integer.parseInt(s1[2]);
		int [] a = new int [n+1];
		if(n!=1) a[1] = Integer.parseInt(s2[1]) - 2;
		for(int i=2;i<=n;i++) {
			if(i==n) {
				a[i] = a[i-1] + k - Integer.parseInt(s2[i-2]) -1;
				break;
			}
			a[i] = Integer.parseInt(s2[i]) - Integer.parseInt(s2[i-2]) - 2 + a[i-1];
		}
		while(q--!=0) {
			String [] s = in.readLine().trim().split(" ");
			int begin = Integer.parseInt(s[0]);
			int end = Integer.parseInt(s[1]);
			long res = 0;
			if(begin==end) {	
				res = k - 1;
			}else if(begin+1==end) {
				res = Integer.parseInt(s2[begin]) - 2 + k - Integer.parseInt(s2[begin-1])-1;
			}else {
				res = a[end-1] - a[begin] + Integer.parseInt(s2[begin]) - 2 + k - Integer.parseInt(s2[end-2])-1;
			}
			out.println(res);
		}
		out.flush();
	}
}
