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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Codeforces {
	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;
		}
	}
//	static Map<Integer, ArrayList<Integer>> map = new HashMap<>();
	//static int[][] dp = new int[100001][1000001];
	
	public static void main(String args[]) {
		FastReader sc = new FastReader();
		// Scanner sc = new Scanner(System.in);
		//System.out.println(java.time.LocalTime.now());
		StringBuilder sb = new StringBuilder();
		
	    int n = sc.nextInt();
		int q = sc.nextInt();
		int k = sc.nextInt();
		int[] arr = new int[n];
		for(int i =0; i<n; i++)arr[i] = sc.nextInt();
		Map<ArrayList<Integer>, Integer> map = new HashMap<>();
		int[] arrr = new int[n];
		for(int i = 0; i<n; i++)arrr[i] = -1;
		if(n>1) {
		arrr[0] = arr[1]-2;
		for(int i = 1; i<n; i++) {
			if(i == n-1) {
				arrr[i] = k - arr[i-1] -1 + arrr[i-1];
			}else {
				arrr[i] = arr[i+1]-arr[i-1] -2 + arrr[i-1];
			}
		}
		}
		
		while(q>0) {
			
			int l = sc.nextInt()-1;
			int r = sc.nextInt()-1;
			
			
			if(l == r)sb.append(k-1+"\n");
			else {
				long ans = arr[l+1]-2;
				ans += k - arr[r-1] -1;
				ans+= arrr[r-1]-arrr[l];
			sb.append(ans + "\n");
			}
			q--;
		}
		
		
		System.out.println(sb);
		
    }
	
//////////nCr////////////////////////////////////////
	

	


///////// SUM OF EACH DIGIT OF A NUMBER ///////////////
public static long digSum(long a) {
	long sum = 0;
	while(a>0) {
		sum += a%10;
		a /= 10;
	}
	
	return sum;
}

///////// TO CHECK NUMBER IS PRIME OR NOT ///////////////
public static boolean isPrime(int n) {
	if(n<=1)return false;
	if(n <= 3)return true;
	if(n%2==0 || n%3==0)return false;
	
	for(int i = 5; i*i<=n; i+=6) {
		if(n%i == 0 || n%(i+2) == 0)return false;
	}
	
	return true;
}

///////// NEXT PRIME NUMBER BIGGER THAN GIVEN NUMBER ///////////////
public static int nextPrime(int n) {
	while(true) {
		n++;
		if(isPrime(n)) break;
			
	}
	
	return n;
}

///////// GCD  ///////////////
public static int gcd(int a, int b) {
	if(b == 0)return a;
	
	return gcd(b, a%b);
}

///////// LCM ///////////////
public static int lcm(int a, int b) {
	return (a*b)/gcd(a,b);
}
}



