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>
#include <string>

typedef long long ll;
typedef long double ldb;
typedef double db;
using namespace std;

#define ff first
#define ss second
#define pb push_back
#define pf push_front
#define ins insert
#define mp make_pair
#define len(s) s.length()
#define forp(i, a, b) for (ll i = a; i <= b; i++)
#define rep(i, n) for (ll i = 0; i < n; i++)
#define ren(i, n) for (ll i = n - 1; i >= 0; i--)
#define forn(i, a, b) for (ll i = a; i >= b; i--)
#define on cout << endl
#define o2(a, b) cout << a << " " << b
#define os cout << " "
#define all(v) v.begin(), v.end()
#define mem(n, m) memset(n, m, sizeof(n))
#define vi vector<int>
#define vl vector<ll>
#define ld long double
#define vld vector<ld>
#define vvi vector<vector<int>>
#define vvl vector<vector<long long>>
#define vvld vector<vector<ld>>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vpii vector<pii>
#define vpll vector<pll>
#define mll map<ll, ll>
#define lb lower_bound
#define ub upper_bound
#define ret return 0
#define present(s, x) (s.find(x) != s.end())
#define cpresent(s, x) (find(all(s), x) != s.end())
#define ford(container, it) for (__typeof(container.begin()) it = container.begin(); it != container.end(); it++)
#define fors(container, it, a, b) for (__typeof(container.begin()) it = a; it != b; it++)
#define d1(x) cout << (x) << endl
#define d2(x, y) cout << (x) << " " << (y) << endl
#define d3(x, y, z) cout << (x) << " " << (y) << " " << (z) << endl
#define d4(a, b, c, d) cout << (a) << " " << (b) << " " << (c) << " " << (d) << endl
#define max3(a, b, c) max(max(a, b), c)
#define min3(a, b, c) min(min(a, b), c)

#define boost ios_base::sync_with_stdio(0)
#define MOD 1000000007
#define EPSILON 1e-9
#define PI 3.14159265358979323846
#define inf 999999999999999999
#define siz 100001
#define SIZ 1000001
#define SIZE 200001

#define pqb priority_queue<int>
#define pqs priority_queue<int, vi, greater<int>>
#define setbits(x) __builtin_popcountll(x)
#define zrobits(x) __builtin_ctzll(x)
#define w(x)  \
    int x;    \
    cin >> x; \
    while (x--)

ll power(ll x, ll y, ll p)
{
    ll res = 1;
    x = x % p;
    while (y > 0)
    {
        if (y & 1)
            res = (res * x) % p;
        y = y >> 1;
        x = (x * x) % p;
    }
    return res;
}
ll pwr(ll x, ll y)
{
    ll res = 1;
    x = x;
    while (y > 0)
    {
        if (y & 1)
            res = (res * x);
        y = y >> 1;
        x = (x * x);
    }
    return res;
}
ll modInverse(ll n, ll p)
{
    return power(n, p - 2, p);
}
ll gcd(ll a, ll b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}
ll lcm(ll a, ll b)
{
    return (b * a) / gcd(a, b);
}
ll fact(ll n)
{
    if (n <= 1)
        return 1;
    return n * fact(n - 1);
}
ll nPr(ll n, ll r)
{
    return fact(n) / fact(n - r);
}
string chain(string s)
{
    string ch = s;
    for (int j = 1; j <= s.size() / 2; j++)
    {
        // d2(s.substr(0,j),s.substr(j,j));
        if (s.substr(0, j) == s.substr(j, j))
        {
            ch = s.substr(0, j);
            break;
        }
    }
    return ch;
}
ll countDigit(ll n)
{
    int count = 0;
    while (n != 0)
    {
        n = n / 10;
        ++count;
    }
    return count;
}
ll lol(ll a, ll b)
{
    ll c=0;
    if(b==1)
        return inf;
    while(a>0)
    {
        a/=b;
        c++;
    }
    return c;
}
void c_p_c()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    c_p_c();
    ll t;
    // cin >> t;
    t = 1;
    while (t-- > 0)
    {
        ll n, q, k;
        cin>>n>>q>>k;
        ll a[n];
        rep(j, n)
        cin>>a[j];
        rep(i, q)
        {
            ll l, r, c;
            cin>>l>>r;
            c=k-a[r-1]+a[l-1]-1+2*(a[r-1]-a[l-1]-1-(r-l-1));
            d1(c);
        }
    }

    return 0;
}