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].
/*input
6 5 10
2 4 6 7 8 9
1 4
1 2
3 5
1 6
5 5
*/

#include <bits/stdc++.h>
#define ll long long

using namespace std;

void run() {
	int n, q, i;
	ll k;
	cin >> n >> q >> k;
	vector<ll> a(n);
	for(auto &x : a)
		cin >> x;
	vector<ll> pref(n + 1, 0);
	for(i=0; i<n; i++) {
		pref[i + 1] = pref[i] + a[i] - (i ? a[i - 1] + 1 : 1) + (i + 1 < n ? (a[i + 1] - a[i] - 1) : 0);
		// cout << pref[i + 1] << " ";
	}
	// cout << endl;
	while(q--) {
		int l, r;
		cin >> l >> r;
		if(l == r) {
			cout << k - 1 << endl;
			continue;
		}
		ll ret = pref[r] - pref[l - 1];
		// cout << "ret: " << ret << endl;
		if(l > 1) {
			ret -= a[l - 1] - a[l - 2] - 1;
			ret += a[l - 1] - 1;
		}
		if(r < n && r > 0) {
			ret -= a[r] - a[r - 1] - 1;
		}
		ret += k - a[r - 1];
		cout << ret << endl;
	}
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(10);
	run();
}
