Replace and Keep Sorted

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].

inputFormat

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).

outputFormat

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].

样例

6 5 10
2 4 6 7 8 9
1 4
1 2
3 5
1 6
5 5

8
9
7
6
9

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