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<bits/stdc++.h>
using namespace std;
#define ll long long int
#define ld long double
#define mem(a,val) memset(a,(val),sizeof((a)))
#define FAST std::ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define decimal(n)  cout << fixed ; cout << setprecision((n));
#define mp make_pair
#define eb emplace_back
#define f first 
#define s second
#define all(v) v.begin(), v.end()
#define endl "\n"
#define lcm(m,n) (m)*((n)/__gcd((m),(n)))
#define rep(i,n) for(ll (i)=0;(i)<(n);(i)++)
#define rep1(i,n) for(ll (i)=1;(i)<(n);(i)++)
#define repa(i,n,a) for(ll (i)=(a);(i)<(n);(i)++)
#define repr(i,n) for(ll (i)=(n)-1;(i)>=0;(i)--)
#define pll pair<ll,ll>
#define mll map<ll,ll>
#define vll vector<ll>
#define sz(x) (ll)x.size()
#define ub upper_bound
#define lb lower_bound
#define pcnt(x) __builtin_popcountll(x)
const long long N=1e9;
const long long NN=1e18;
const int32_t M=1e9+7;
const int32_t MM=998244353;
template<typename T,typename T1>T maxn(T &a,T1 b){if(b>a)a=b;return a;}
template<typename T,typename T1>T minn(T &a,T1 b){if(b<a)a=b;return a;}

void solve()
{
  //code begins from here//
  ll n,q,k;
  cin>>n>>q>>k;
  ll a[n+1];
  rep1(i,n+1)cin>>a[i];
  rep(i,q)
  {
      ll l,r;
      cin>>l>>r;
      ll ans=k-2*(r-l+1)+a[r]-a[l]+1;
      cout<<ans<<endl;
  }
}

signed main()
{
FAST
//freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
int testcase=1;
//cin>>testcase;
while(testcase--) solve();
return 0;
}
