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].
'''
Aaditya Upadhyay
                          ud$$$**$$$$$$bc.
                       u@**"        4$$$$$$Nu
                     J                ""#$$$$$r
                    @                       $$$b
                  .F                        ^*3$$$
                 :% 4                         J$$N
                 $  :F                       :$$$$$
                4F  9                       J$$$$$$$
                4$   k             4$$$bed$$$$$$$$$
                $r  'F            $$$$$$$$$$$$$$$$r
                $$$   b.           $$$$$$$$$$$$$$$$N
                $$$$k 3eeed$b    $$Euec."$$$$$$$$$
 .@$**N.        $$$$$" $$$$$F'L $$$$$$$$$$$  $$$$$$$
 :$L  'L       $$$$$ 4$$$$$$  * $$$$$$$$$F  $$$$$F         edNc
@$$$N  ^k      $$$$$  3$$$$*%   F4$$$$$$$   $$$$$"        d"  zN
$$$$$$   ^k     '$$$"   #$$F   .$  $$$$c.u@$$$          J"  @$$$r
$$$$$$b   *u    ^L            $$  $$$$$$$$$$$u@       $$  d$$$$$$
 ^$$$$$$.    "NL   "N. z@*     $$$  $$$$$$$$$$$$P      P  d$$$$$$$
    ^"*$$$b   '*L   9E      4$$$  d$$$$$$$$$$$"     d*   J$$$$r
         ^$$$u  '$.  $$L     "#" d$$$$$$".@$$    .@$"  z$$$$*"
           ^$$$$. ^N.3$$$       4u$$$$$$$ 4$$$  u$*" z$$$"
             '*$$$$$$$$ *b      J$$$$$$b u$P $"  d$P
                #$$$$$$ 4$ 3*$"$*$ $"$'c@@$$$$ .u@$$P
                  "$$$$  ""F~$ uNr$$$^&J$$$F $$$$#
                    "$$    "$$bd$.W$$$$$$$F $$"
                      ?k         ?$$$$$$$$$$F'*
                       9$bL     z$$$$$$$$$$F
                        $$$$    $$$$$$$$$$$$$
                         '#$c  '$$$$$$$$$"
                          .@"#$$$$$$$$$$$b
                        z*      $$$$$$$$$$$N.
                      e"      z$$"  #$$k  '*$$.
                  .u*      u@P"      '#$c   "$c
           u@$*"""       d$$"            "$$u  ^*$b.
         :F           JP"                ^$$c   '"$$$$$bL
        d$$  ..      @$#                      #$b         '#$
        9$$$$$b   4$$                          ^$k         '$
         "$""b u$$                             '$    d$$$$P
           'F $$$$$"                              ^b  ^$$$b$
            'W$$$$"                                'b@$$$$"
                                                     ^$$$*
'''
from sys import stdin, stdout
from collections import *
from math import gcd, floor, ceil
def st(): return list(stdin.readline().strip())


def li(): return list(map(int, stdin.readline().split()))
def mp(): return map(int, stdin.readline().split())
def inp(): return int(stdin.readline())
def pr(n): return stdout.write(str(n)+"\n")


mod = 1000000007
INF = float('inf')


def solve():
    n, q, k = mp()
    A = li()
    for i in range(q):
        l, r = mp()
        pr(k - (r - l + 1) + (A[r - 1] - A[l - 1] + 1 - (r - l + 1)))

for _ in range(1):
    solve()
