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].


//package _701;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.nio.file.Paths;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main2 {

	public Main2() throws FileNotFoundException {

//		File file = Paths.get("input.txt").toFile();
//		if (file.exists()) {
//			System.setIn(new FileInputStream(file));
//		}
		long t = System.currentTimeMillis();

		FastReader reader = new FastReader();

		int n = reader.nextInt();
		int q = reader.nextInt();
		int k = reader.nextInt();

		int[] left = new int[n];
		int[] right = new int[n];
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = reader.nextInt();
		}

		for (int i = 1; i < n; i++) {
			left[i] = a[i] - a[i - 1] - 1;
		}
		// System.out.println("LEFT:" + Arrays.toString(left));
		for (int i = n - 2; i >= 0; i--) {
			right[i] += a[i + 1] - a[i] - 1;
		}
		// System.out.println("RIGHT:" + Arrays.toString(right));
		for (int i = 1; i < n; i++) {
			left[i] += left[i - 1];
		}
		for (int i = 1; i < n; i++) {
			right[i] += right[i - 1];
		}

		// System.out.println("DP:"+Arrays.toString(dp));

		for (int i = 0; i < q; i++) {

			int from = reader.nextInt() - 1;
			int to = reader.nextInt() - 1;

			int sum = 0;
			if (from > 0) {
				sum += left[to] - left[from];
			} else {
				sum += left[to];
			}
			if (to > 0) {
				if (from > 0) {
					sum += right[to - 1] - right[from - 1];
				} else {
					sum += right[to - 1];
				}
			}

			// System.out.println("1:"+sum);
//			int dpsum=dp[to];
//			if(from>0) {
//				dpsum-=dp[from-1];
//			}
//			8
//			9
//			7
//			6
//			9

			sum += a[from] - 1;
			sum += k - a[to];

			System.out.println(sum);

		}

		// System.out.println("TIME: "+(System.currentTimeMillis()-t));
	}

	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;
		}
	}

	public static void main(String[] args) throws FileNotFoundException {
		new Main2();
	}

}
