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 <cstdio>
#include <string>
#include <algorithm>
#include <sstream>
#include <cmath>
#include <iomanip>
#include <stack>
#include <queue>
#include <deque>
#include <limits>
#include <set>
#include <map>
#include <cctype>
#include <fstream>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#include <cstring>
#include <functional>
#include <bitset>
#include <random>

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define size_t ll
#define pii pair<int, int>
#define SSS std::ios::sync_with_stdio(false), std::cin.tie(0), std::cout.tie(0)
bool _Debug_Flag = 1;
#define DEBUG                                                                            \
    {                                                                                    \
        cout << endl                                                                     \
             << (_Debug_Flag ? R"(\\\\\\debug//////)" : R"(//////debug\\\\\\)") << endl; \
        _Debug_Flag = !_Debug_Flag;                                                      \
    }
#define caseT  \
    ll T;      \
    cin >> T;  \
    cin.get(); \
    while (T--)
#define ra(i, a, b) for (ll i = (a); i <= (b); i++)
#define rr(i, a, b) for (ll i = (a); i >= (b); i--)
#define rep(i, a, b) for (ll i = (a); i < (b); i++)
#define rect(n, m) ra(i, 1, n) ra(j, 1, m)

#define cti(c) int(c - '0')
#define itc(i) char(i + '0')

using namespace std;

const int MAXN = 1e5 + 10;
const int MOD = 1e9 + 7;
const ll INF = 0x3f3f3f3f;
const ld EPS = 1e-7;
////////////////////////////////////////////////////////////////
int a[MAXN];
////////////////////////////////////////////////////////////////

int main()
{
    SSS;
    int n, k, q;
    cin >> n >> q >> k;
    ra(i, 1, n)
            cin >>
        a[i];
    while (q--)
    {
        int l, r;
        cin >> l >> r;
        cout << k + a[r] - (a[l] - 1) - (r - l + 1) * 2 << endl;
    }

    return 0;
}
////////////////////////////////////////////////////////////////