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.*;

public class B {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
			FastScanner sc = new FastScanner();
	
			int n = sc.nextInt();
			int q = sc.nextInt();
			int k = sc.nextInt();
			
			int[] a = new int[n + 1];
			
			for(int i = 1 ; i <= n ; i++) {
				a[i] = sc.nextInt();
			}
			
			
			long[] sumtill = new long[n + 1];
			
			for(int i = 1 ;i <= n ; i++) {
				long left = a[i] - a[i - 1] - 1;
				long right = (i == n) ? k - a[i] : a[i + 1] - a[i] - 1;
				
				
				sumtill[i] = left + right;
				sumtill[i] += sumtill[i - 1];
				
				//System.out.println(left + right);
				
			}
			while(q-- > 0){
				int l = sc.nextInt() ;
				int r = sc.nextInt();
				
				
				long sol = sumtill[r] - sumtill[l - 1];
				
				sol -= (l == 0)? a[l] - 1 :a[l] - a[l - 1] - 1;
				sol -= (r == n) ? k - a[r] : a[r + 1] - a[r] - 1;
				
				sol += a[l] - 1 ;
				sol +=  k - a[r] ;
				System.out.println(sol);
				
			}
			System.out.println();
		
		
		
		
			

	}
	
	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());
		}
	}

}
