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.*;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		StringBuilder sb = new StringBuilder();
		
		try {
			st = new StringTokenizer(br.readLine());
			int n = Integer.parseInt(st.nextToken());
			int q = Integer.parseInt(st.nextToken());
			int k = Integer.parseInt(st.nextToken());
			int[] seq = new int[n];
			
			st = new StringTokenizer(br.readLine());
			for(int i = 0; i < n; i++) {
				seq[i] = Integer.parseInt(st.nextToken());
			}
			
			while(q --> 0) {
				st = new StringTokenizer(br.readLine());
				int l = Integer.parseInt(st.nextToken());
				int r = Integer.parseInt(st.nextToken());
				int ans = 0;
				
				if(r - l == 0) {
					ans += (n - 1);
					sb.append(k - 1).append('\n');
					continue;
				}
				
				ans += (seq[l] - 2);
				ans += (k - seq[r - 2] - 1);
				
				if(r - l > 2) {
					ans += (seq[r - 1] + seq[r - 2] - seq[l] - seq[l - 1]);
					ans -= ((r - l - 1) * 2);
				}
				else if(r - l == 2) {
					ans += (seq[r - 1] - seq[l - 1] - 2);
				}
				
				
				sb.append(ans).append('\n');
				
			}
			System.out.println(sb.toString());
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

}
