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 tank {
     
        //static StringBuilder IO = new StringBuilder();
     
        //static final Scanner scan = new Scanner(System.in);
     
        static final FastScanner fs = new FastScanner();
     
        public static void main(String[] args) {
    //        int t = fs.nextInt();
    //        while(t-->0){
    //            SLV();
    //        }
     
            SLV();
            //System.out.println(IO);
        }
     
        static void SLV(){
            int n = fs.nextInt(), q = fs.nextInt(), k = fs.nextInt();
            int[] arr = fs.readArray(n);
            int [][] qu = new int[q][2];
     
            for (int i = 0; i < q; i++) {
                qu[i][0] = fs.nextInt();
                qu[i][1] = fs.nextInt();
            }
     
            long[] dp = new long[n+1];
            dp[0] = 0;
     
            for (int i = 0; i < n; i++) {
                dp[i+1] = (i == n-1 ? k : arr[i+1]) -
                        (i == 0 ? 1 : arr[i-1]) - 2;
                if(dp[i+1] < 0) dp[i+1] = 0;
                dp[i+1] += dp[i];
            }
     
            for (int i = 0; i < q; i++) {
                long ans = dp[qu[i][1] - 1] - dp[qu[i][0]];
                if(qu[i][0] == qu[i][1]) {
                    System.out.println(k-1);
                    continue;
                }
                ans += arr[qu[i][0]] - 2;
                ans += k - arr[qu[i][1] - 2] - 1;
                System.out.println(ans);
            }
        }
     
        static class FastScanner {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            StringTokenizer st=new StringTokenizer("");
            String next() {
                while (!st.hasMoreTokens())
                    try {
                        st=new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                return st.nextToken();
            }
     
            int nextInt() {
                return Integer.parseInt(next());
            }
     
            int[] readArray(int n) {
                int[] a=new int[n];
                for (int i=0; i<n; i++) a[i]=nextInt();
                return a;
            }
            long nextLong() {
                return Long.parseLong(next());
            }
     
            double nextDouble() { return Double.parseDouble(next()); }
        }
    }