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 ReplaceAndKeepSorted {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	public static void main(String[] args) throws IOException {
		int n = readInt(), q = readInt(), k = readInt();
		
		int[] arr = new int[n];
		for (int i = 0; i < n; i ++) arr[i] = readInt();
		
		long[] pfs = new long[n];
		for (int i = 1; i < n - 1; i ++) {
			pfs[i] = pfs[i - 1] + arr[i + 1] - arr[i - 1] - 2;
		}

		for (int i = 0; i < q; i ++) {
			int l = readInt() - 1, r = readInt() - 1;
			
			long ans = 0;
			if (r - l == 0) {
				ans = k - 1;
			} else if (r - l == 1) {
				ans += arr[l + 1] - 2;
				ans += k - arr[r - 1] - 1;
			} else {
				ans += arr[l + 1] - 2;
				ans += k - arr[r - 1] - 1;
				ans += pfs[r - 1] - pfs[l];
			}
			
			System.out.println(ans);
		}
	}

	static String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) 
			st = new StringTokenizer(br.readLine().trim());
		return st.nextToken();
	}
	static long readLong() throws IOException {
		return Long.parseLong(next());
	}
	static int readInt() throws IOException {
		return Integer.parseInt(next());
	}
	static double readDouble() throws IOException {
		return Double.parseDouble(next());
	}
	static char readCharacter() throws IOException {
		return next().charAt(0);
	}
	static String readLine() throws IOException {
		return br.readLine().trim();
	}
}