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 final int M = 1000000007;
	static FastReader in = new FastReader();
//	static PrintWriter out = new PrintWriter(System.out);
//	static Scanner in = new Scanner(System.in);
//	File file = new File("input.txt");
//	Scanner in = new Scanner(file);
//	PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
//	Arrays.sort(arr, Comparator.comparingDouble(o -> o[0]));
	
	public static void main(String[] args) {
		
//		int t = in.nextInt();
//		while(t-- > 0) solve();
		solve();
	}
	static void solve() {		
		//write your code here
		int n = in.nextInt(), q = in.nextInt(), k = in.nextInt();
		int[] a = new int[n+1];
		for(int i = 1; i<=n; i++) a[i] = in.nextInt();
		int[] p = new int[n+5];
		for(int i = 2; i<n; i++) p[i] = p[i-1] + (a[i]-a[i-1]-1) + (a[i+1]-a[i]-1);
		while(q-- > 0) {
			int l = in.nextInt(), r = in.nextInt();
			if(l==r) {
				System.out.println(k-1);
				continue;
			}
			if(l == r-1) {
				int res = 0;
				if(a[r] != 1) res += a[r]-2;				
				if(a[r] != k) res += k-1-a[l];
				System.out.println(res);
				continue;
			}
			int atp = p[r-1] - p[l];
			if(a[l+1]!=1) {
				atp += (a[l+1]-1) - 1;
			}
			if(a[r-1] != k) atp+= k-1-a[r-1];
			System.out.println(atp);
		}
		
		
	}
	
	static void sieve(int n, boolean[] prime)
    {
        for (int i = 0; i <= n; i++)
            prime[i] = true;
 
        for (int p = 2; p * p <= n; p++) 
        {
            if (prime[p] == true) 
            {
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
	static int gcd(int a, int b) {
		if(b==0) return a;
		return gcd(b, a%b);
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new
					InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}