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

### A ###
# for _ in range(int(input())):
#     n, k = map(int, input().split())
#     s = k
#     l = [999999999, 9999999]
#     while l[-2] > l[-1]:
#         a = k - s
#         if k == 1:
#             k += 1
#             a += 1
#         t = n
#         while t:
#             t //= k
#             a += 1
#         k += 1
#         l.append(a)
#     print(min(l))

### B ####
n, q, k = map(int, input().split())
l = list(map(int, input().split()))
new_l = [0] * n
m_val = [0] * n
mi_val = [0] * n
s = [0]*n
for i in range(n):
    if i < n-1:
        m_val[i] = min(l[i+1] - 1, k)
    else:
        m_val[i] = max(k, l[i])
for i in range(n):
    if i !=0:
        mi_val[i] = min(l[i-1]+1, l[i])
    else:
        mi_val[i] = min(1, l[i])

for i in range(n):
    new_l[i] = m_val[i] - mi_val[i]

s[0] = new_l[0]
for i in range(n):
    s[i] = s[i-1]+ new_l[i]

for i in range(q):
    x, y = map(int, input().split())
    if x == y:
        print(k-1)
    else:
        ad1 = m_val[x-1] - 1
        ad2 = k - mi_val[y-1]
        ad3 = s[y-2] - s[x-1]
        print(ad1 + ad2 + ad3)