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].
n,q,k = map(int, input().strip().split(' '))
lst = list(map(int, input().strip().split(' ')))
l=[]
c=0
if n!=1:
    for i in range(n):
        if i==0:
            c+=lst[i+1]-2
        elif i==n-1:
            c+=k-lst[i-1]-1
        else:
            c+=lst[i+1]-lst[i-1]-2    
        l.append(c)
for i in range(q):
    li,r = map(int, input().strip().split(' '))
    if li==r:
        print(k-1)
    elif li==1 and r==n:
        print(l[-1])
    elif li==1:
        s=l[r-2]+(k-lst[r-2]-1)
        print(s)
    elif r==n:
        s=l[-1]-l[li-1]+lst[li]-2
        print(s)
    else:
        if r==li+1:
            s=k-lst[li-1]+lst[r-1]-1-2
        else:
            s=l[r-2]-l[li-1]+k-lst[r-2]+lst[li]-1-2
        print(s)
        