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 MyCpClass
{
    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)
    {
        FastReader fs=new FastReader();
        int n = fs.nextInt();
        int q = fs.nextInt();
        int k = fs.nextInt();
        int []a = new int[n+1];
        for(int i=1; i<=n; i++)
            a[i] = fs.nextInt();
        
        int []count = new int[n+1];
        for(int i=1; i<=n; i++) {
            if(i == 1 && (i+1) <= n)
                count[i] += (a[i+1] - 2);
            else if(i == n)
                count[i] += (k - 1 - a[i-1]);
            else
                count[i] += (a[i+1] - a[i-1] - 2);
        }
        
        int []sum = new int[n+1];
        for(int i=1; i<=n; i++)
            sum[i] = sum[i-1] + count[i];
        
        while(q-- > 0){
            int l = fs.nextInt();
            int r = fs.nextInt();
            int cnt = 0;
            
            if(l == r)
                cnt += (k - 1);
            else if(r - l == 1){
                cnt += (a[l+1] - 2);
                cnt += (k - 1 - a[r-1]);
            }
            else{
                cnt += (a[l+1] - 2);
                cnt += (k - 1 - a[r-1]);
                cnt += (sum[r-1] - sum[l]);
            }
            
            System.out.println(cnt);
        }
    }
}