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 contest;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class B {
	private static PrintWriter out = new PrintWriter(System.out);

	public static void solve() {
		In in = new In();
		int n = in.ni();
		int Q = in.ni();
		int k = in.ni();
		long[] a = in.nla(n);
		long[] pre = new long[n];
		pre[0] = a[0] - 1;
		for (int i = 1; i < n; i++)
			pre[i] = pre[i - 1] + a[i] - a[i - 1] - 1;
		long[] suf = new long[n];
		suf[n - 1] = k - a[n - 1];
		for (int i = n - 2; i >= 0; i--)
			suf[i] = suf[i + 1] + a[i + 1] - a[i] - 1;

		
//		System.out.println(Arrays.toString(pre));
//		System.out.println(Arrays.toString(suf));
		for (int q = 0; q < Q; q++) {
			int l = in.ni() - 1;
			int r = in.ni() - 1;
//			System.out.println(sum(l + 1, r, pre) + " " + sum(l, r - 1, suf) + " " + ( a[l] - 1)  + " "+ (k - a[r]));
			long ans = pre[r] - pre[l] + suf[l] - suf[r] + a[l] - 1 + k - a[r]; 
			out.println(ans);
		}
	}
	
	static int sum(int from, int to, int[] cum) {
		return cum[to] - (from == 0 ? 0 : cum[from - 1]);
	}

	static long sum(int from, int to, long[] cum) {
		if (from > to) return 0;
		return cum[to] - (from == 0 ? 0 : cum[from - 1]);
	}

	public static void main(String[] args) throws IOException {
		// long start = System.nanoTime();
		solve();
		// System.out.println("Elapsed: " + (System.nanoTime() - start) / 1000000 +
		// "ns");
		out.flush();
	}

	@SuppressWarnings("unused")
	private static class In {
		final private static int BUFFER_SIZE = 1024;
		private byte[] buf;
		private InputStream is;
		private int buflen;
		private int bufptr;

		public In() {
			is = System.in;
			buf = new byte[BUFFER_SIZE];
			buflen = bufptr = 0;
		}

		public In(String input) {
			is = new ByteArrayInputStream(input.getBytes());
			buf = new byte[BUFFER_SIZE];
			buflen = bufptr = 0;
		}

		public int readByte() {
			if (bufptr >= buflen) {
				try {
					buflen = is.read(buf);
				} catch (IOException ioe) {
					throw new InputMismatchException();
				}
				bufptr = 0;
			}
			if (buflen <= 0)
				return -1;
			return buf[bufptr++];
		}

		public boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		public int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		/* Next character */
		public char nc() {
			return (char) skip();
		}

		/* Next double */
		public double nd() {
			return Double.parseDouble(ns());
		}

		/* Next string */
		public String ns() {
			final StringBuilder sb = new StringBuilder();
			int b = skip();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		/* Next integer */
		public int ni() {
			boolean minus = false;
			int num = 0;
			int b;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			while (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
				b = readByte();
			}
			return minus ? -num : num;
		}

		/* Next long */
		public long nl() {
			boolean minus = false;
			long num = 0;
			int b;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			while (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
				b = readByte();
			}
			return minus ? -num : num;
		}

		/* Next integer 1D array */
		public int[] nia(int n) {
			final int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				arr[i] = ni();
			return arr;
		}

		/* Next long 1D array */
		public long[] nla(int n) {
			final long[] arr = new long[n];
			for (int i = 0; i < n; i++)
				arr[i] = nl();
			return arr;
		}

		/* Next string 1D array */
		public String[] nsa(int n) {
			final String[] arr = new String[n];
			for (int i = 0; i < n; i++)
				arr[i] = ns();
			return arr;
		}

		/* Next char 1D array */
		public char[] nca(int n) {
			final char[] arr = new char[n];
			for (int i = 0; i < n; i++)
				arr[i] = nc();
			return arr;
		}

		/* Next double 1D array */
		public double[] nda(int n) {
			final double[] arr = new double[n];
			for (int i = 0; i < n; i++)
				arr[i] = nc();
			return arr;
		}

		/* Next integer matrix */
		public int[][] nim(int n, int m) {
			final int[][] arr = new int[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = ni();
			return arr;
		}

		/* Next long matrix */
		public long[][] nlm(int n, int m) {
			final long[][] arr = new long[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nl();
			return arr;
		}

		/* Next string matrix */
		public String[][] nsm(int n, int m) {
			final String[][] arr = new String[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = ns();
			return arr;
		}

		/* Next char matrix */
		public char[][] ncm(int n, int m) {
			final char[][] arr = new char[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nc();
			return arr;
		}

		/* Next double matrix */
		public double[][] ndm(int n, int m) {
			final double[][] arr = new double[n][m];
			for (int i = 0; i < n; i++)
				for (int j = 0; j < m; j++)
					arr[i][j] = nd();
			return arr;
		}

		public static void log(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
	}

}
