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B. Replace and Keep Sorted

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$[a_{l_i},a_{l_i+1}\ldots,a_{r_i}]$$$.

Input

The 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 $$$l_i$$$, $$$r_i$$$ ($$$1 \leq l_i \leq r_i \leq n$$$).

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 $$$[4,5]$$$: $$$[1,5],[2,5],[3,5]$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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