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].
#include <iostream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <bitset>
#include <string>
#include <cstring>
#include <cmath>
#include <cstdio>
#define all(v) (v).begin(), (v).end()
#define unq(v) (v).erase(unique(all(v)), (v).end())
#define ii int, int
#define li int, int
#define ll2 ll, ll
#define vec vector
#define pii pair <int, int>
#define pli pair <ll, int>
#define pil pair <int, ll>
#define pll2 pair <ll, ll>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define MULTI int T; cin >> T; while(T--)
#define sqr(x) ((x) * (x))
#define test cerr << '!' << endl;
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

void main0 ();
int main () {
	clock_t start, end;
	#ifndef ONLINE_JUDGE
		freopen("C:\\Users\\98497\\Desktop\\code\\file.in", "r", stdin);
		start = clock();
	#endif
	ios::sync_with_stdio(false);
	main0();
	#ifndef ONLINE_JUDGE
		end = clock();
		cout << "( "<<(end - start) << " ms )" << endl;
		fclose(stdin);
	#endif
	return 0;
}

const int dx[8] = {0, 1, -1, 0, 1, 1, -1, -1};
const int dy[8] = {1, 0, 0, -1, 1, -1, -1, 1};
const int N = 2e5 + 5;
const int M = 1e5;
const int INF = 0x3f3f3f3f;
const ll INFF = 0x3f3f3f3f3f3f3f3f;
const int mod = 998244353;
const double eps = 1e-6;
const double Pi = acos(-1.0);

int a[N];

void main0 () {
	int n, q, k;
	cin >> n >> q >> k;
	for (int i = 1;i <= n;++i) {
		cin >> a[i];
	}
	
	for (int i = 1;i <= q;++i) {
		int l, r;
		cin >> l >> r;
		cout << k + (a[r] - a[l] + 1) - 2 * (r - l + 1) << endl;
	}
}
