B. Replace and Keep Sortedtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven 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 \leq 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}\ldots,a_{r_i}]. InputThe first line contains three integers n, q and k (1\leq n, q \leq 10^5, n\leq k \leq 10^9) — the length of array a, the number of queries and number k.The second line contains n integers a_1, a_2, \ldots,a_n (1 \leq a_i \leq k). This array is strictly increasing  — a_1 < a_2 < \ldots < a_n.Each of the following q lines contains two integers l_i, r_i (1 \leq l_i \leq r_i \leq n).OutputPrint q lines. The i-th of them should contain the answer to the i-th query.ExamplesInput
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
NoteIn 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].
4 2 5
1 2 4 5
2 3
3 4

4 3 
['dp', 'implementation', 'math', '*1200']