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.util.*;
import java.io.*;


public class Main {
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(
                new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0,
                                 BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
  //System.out.println("YES");
//System.out.println("NO");
 
//int n=sc.nextInt();
//int a[]=new int[n];
//for(int i=0;i<n;i++)
//a[i]=sc.nextInt();
 
//int n=sc.nextInt();
//long a[]=new long[n];
//for(int i=0;i<n;i++)
//a[i]=sc.nextLong();
 
//System.out.println();

//String str=sc.next();
//long n=sc.nextLong();


	public static void main(String[] args) throws IOException{
	//	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		Reader sc=new Reader();
		PrintWriter out=new PrintWriter(System.out);
	//	int t = sc.nextInt();
	//	while(t-->0) {
	    long n=sc.nextLong();
	    long q=sc.nextLong();
	    long k=sc.nextLong();
	    long a[]=new long[(int)n];
	    long length[]=new long[(int)n];
       for(int i=0;i<n;i++)
       a[i]=sc.nextLong();
	     for(int i=0;i<n;i++){
        if(i==0){
            if(n!=1){
                length[i]=a[1]-2;
            }
        }
        if(i!=0&&i!=n-1){
            length[i]=a[i+1]-a[i-1]-2;
        }
    }
    long pre[]=new long[(int)n];
    pre[0]=0;
    for(int i=1;i<n-1;i++){
        pre[i]=pre[i-1]+length[i];
    }
    while(q-->0){
        int l,r;
        l=sc.nextInt();
        r=sc.nextInt();
        l--;
        r--;
        if(l==r)
        out.println(k-1);
        else{
            long ans=0;
             ans=a[l+1]-2+k-a[r-1]-1;
            ans += pre[r-1]-pre[l];
            out.println(ans);
        }
    }
	    
	//	}
		
		out.flush();
		out.close();
	}
}
