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].
#   Author: yumtam
#   Created at: 2021-03-18 23:55

def solve():
    n, q, k = input_as_list()
    a = input_as_list()
    queries = [input_as_list(-1) for _ in range(q)]

    free = [0]*n
    for i in range(1, n-1):
        free[i] = a[i+1] - a[i-1] - 2

    psum = [0]
    for x in free:
        psum.append(psum[-1]+x)

    def get(l, r):
        if l < r:
            return psum[r] - psum[l]
        return 0

    for l, r in queries:
        if l == r:
            print(k-1)
        else:
            lb = a[l+1] - 2
            rb = k - a[r-1] - 1
            ans = lb + get(l+1, r) + rb
            print(ans)


import sys, os, io
input = lambda: sys.stdin.readline().rstrip('\r\n')
stdout = io.BytesIO()
sys.stdout.write = lambda s: stdout.write(s.encode("ascii"))

def input_as_list(offset=0):
    return [int(t)+offset for t in input().split()]

solve()

os.write(1, stdout.getvalue())
