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].
function test() {
    // 第一行输入
    var arr = readline().split(' ');

    var len = parseInt(arr[0], 10)
    var inputLines = parseInt(arr[1], 10)
    var MIN = 1
    var MAX = parseInt(arr[2], 10)


    // 第二行输入
    var list = readline().split(' ')
    list = list.map(function (item) {
        return parseInt(item, 10)
    })

    // 区间处理
    var input = []

    for (var i = 0; i < inputLines; i++) {
        input.push(readline().split(' '))
    }

    // 处理函数
    function count(left, right) {   
        len = right - left + 1
        leftValue = list[left - 1]
        rightValue = list[right - 1]

        result = (MAX - rightValue) + (leftValue - MIN) + (rightValue - leftValue - len + 1) * 2

        return result
    }

    for (var i = 0; i < input.length; i++) {
        print(count(parseInt(input[i][0], 10), parseInt(input[i][1], 10)))
    }
}

test()
  	  	    				 	 	 	  	 				 		