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].
#pragma region
#include <bits/stdc++.h>
#define endl '\n'
#define fastIO ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
#define prec fixed<<setprecision(9)
#define all(x) x.begin(),x.end()
using ll = long long;
using namespace std;
int mod = 1e9+7;

string to_string(string& s) {return '"'+s+'"';}
string to_string(bool& b) {return b?"true":"false";}
string to_string(const char* s) {string t; return to_string(t=s);}
template <class A, class B> string to_string(pair<A, B>& p) {return "("+to_string(p.first)+", "+to_string(p.second)+")";}
template <class A> string to_string(A& v) {string s; for (auto &x : v) s+=(s.empty()?"":", ")+to_string(x); return "{"+s+"}";}
template<class... Ts> void _debug(Ts&... args){(..., (cerr<<" "<<to_string(args))); cerr<<endl;}
#define debug(args...) cerr<<__LINE__<<" ["<<#args<<"]:", _debug(args)
#pragma endregion

int main()
{
    fastIO
    int n,q,k; cin>>n>>q>>k;
    vector<int> arr(n); for(auto& i:arr) cin>>i;
    vector<ll> dp(n,0);
    for(int i=0;i<n;i++){
        ll prev = (i==0 ? 1 : arr[i-1] + 1);
        ll next = (i==n-1 ? k : arr[i+1] - 1);
        dp[i] = (i==0 ? 0LL : dp[i-1]) + next-prev;
    }
    for(int i=0;i<q;i++){
        int l,r; cin>>l>>r; l--; r--;
        ll mid = (r>l+1 ? dp[r-1] - dp[l] : 0);
        ll left = (l+1<=r ? arr[l+1] - 1 : k) - 1;
        ll right = 0; if(l!=r) right = k - (arr[r-1] + 1);
        cout<<left+mid+right<<endl;
    }
}