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 sys
def get_array(): return list(map(int , sys.stdin.readline().strip().split()))
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip()

# for _ in range(int(input())):
n,q,k = get_ints()
a = get_array()
arr = [0]*n
if n!=1:
    for i in range(len(a)):
        if (i==0):
            arr[i] = a[i] - 1+ a[i+1] - a[i] -1
        elif(i==len(a)-1):
            arr[i] = a[i] - a[i-1] -1 + k+1- a[i] -1

        else:
            arr[i] = a[i] - a[i-1] -1  + a[i+1] - a[i] -1
ak = []
s= 0
for i in range(len(arr)):
    s+=arr[i]
    ak.append(s)
# print(arr)
# print(ak)
for i in range(q):
    l,r = get_ints()
    if(n==1):
        print(k-1)
        continue
    if(l==r):
        print(k-1)
        continue
    l-=1
    r-=1
    # print(ak[r-1],ak[l])
    mid = ak[r-1]-ak[l]
    right = k - a[r-1] -1
    left = a[l+1] -1-1
    # print("fkjbf = ",mid,  left, right)
    print(mid+right+left)