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 fast ios_base::sync_with_stdio(false);  cin.tie(NULL); cout.tie(NULL);
#define scan(a,n) for(long long int index=0;index<n;index++) cin>>a[index];
#define print(a,n) for(long long int index=0;index<n;index++) cout<<a[index]<<" ";cout<<endl;
#define mod 1000000007
#define pb push_back
#define mp make_pair
#define ss second
#define ff first
#define vli vector<long long int>
#define vlli vector<pair<long long int,long long int>>
#define vsi vector<string>
#define all(n) n.begin(),n.end()
#define forn(i,a,b) for(i=a;i<b;i++)
ll mul(ll x,ll y){  return (x*y)%mod;}
ll power(ll x, ll y) {ll res = 1; x %= mod;
 while (y) {if (y & 1)res = mul(res, x); y >>= 1; x = mul(x, x);} return res;}
ll mod_inv(ll x) {return power(x, mod - 2);}
ll fact(ll n) {ll res = 1; for (ll i = 2; i <= n; i++) res = mul(res , i); return res; } 
ll nCr(ll n, ll r) { return mul(fact(n),mod_inv(mul(fact(r),fact(n - r))));} 

 
int main() {
  fast;
  #ifndef ONLINE_JUDGE
  freopen("input.txt","r",stdin);
  freopen("output.txt","w",stdout);
  #endif
  ll t=1;
  // cin>>t;
  while(t--){
     ll n, q, k;
	cin>>n>>q>>k;
	vli a(n), p(n, 0);
	scan(a, n);
	ll z=k,i;
	for(i=n-1;i>=0;i--){
		ll x=z-a[i];
		if(i>0){
			x+=a[i]-a[i-1]-1;
		} else {
			x+=a[i]-1;
		}
		p[i]=x;
		z=a[i]-1;
	}
	for(i=1;i<n;i++){
		p[i]+=p[i-1];
	}
	ll x, y;
	while(q--){
		cin>>x>>y;
		
		ll lx, rx;
		rx=p[y-1];
		if(x-1==0){
			lx=0;
		} else {
			lx=p[x-2];
		}
		ll ans=rx-lx;
		
		if(y-1<n-1){
			ans+=k-a[y]+1;
		}
		if(x-1>0){
			ans+=a[x-2];
		}
		cout<<ans<<endl;
	}


  	
  }
return 0;    
 }  