Problem: There are N points on a number line, i-th of which is placed on coordinate X_i. These points are numbered in the increasing order of coordinates. In other words, for all i (1 \leq i \leq N-1), X_i < X_{i+1} holds. In addition to that, an integer K is given.

Process Q queries.

In the i-th query, two integers L_i and R_i are given. Here, a set s of points is said to be a good set if it satisfies all of the following conditions. Note that the definition of good sets varies over queries.

* Each point in s is one of X_{L_i},X_{L_i+1},\ldots,X_{R_i}.
* For any two distinct points in s, the distance between them is greater than or equal to K.
* The size of s is maximum among all sets that satisfy the aforementioned conditions.



For each query, find the size of the union of all good sets.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 10^9
* 0 \leq X_1 < X_2 < \cdots < X_N \leq 10^9
* 1 \leq Q \leq 2 \times 10^5
* 1 \leq L_i \leq R_i \leq N
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
X_1 X_2 \cdots X_N
Q
L_1 R_1
L_2 R_2
\vdots
L_Q R_Q


Output

For each query, print the size of the union of all good sets in a line.

Examples

Input

5 3
1 2 4 7 8
2
1 5
1 2


Output

4
2


Input

15 220492538
4452279 12864090 23146757 31318558 133073771 141315707 263239555 350278176 401243954 418305779 450172439 560311491 625900495 626194585 891960194
5
6 14
1 8
1 13
7 12
4 12


Output

4
6
11
2
3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define int long long
// #define endl '\n'

vector<int> zf(string s) {
    int n = (int)s.size();
    vector<int> z(n);
    int l = 0, r = 0;
    z[0] = 0;
    for (int i = 1; i < n; i++) {
        if (i <= r)
            z[i] = min(r - i + 1, z[i - l]);
        while (i + z[i] < n && s[i+z[i]] == s[z[i]]) z[i]++;
        if (i + z[i] - 1 > r) {
            l = i; r = i + z[i] - 1;
        }
    }
    return z;
}

vector<int> pf(string s) {
    int n = (int)s.size();
    vector<int> p(n);
    p[0] = 0;
    for (int i = 1; i < n; i++) {
        p[i] = p[i - 1];
        while (p[i] && s[p[i]] != s[i]) {
            p[i] = p[p[i] - 1];
        }
        if (s[p[i]] == s[i]) p[i]++;
    }
    return p;
}

int32_t main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n, k; cin >> n >> k;
    vector<int> x(n);
    for (int i = 0; i < n; i++) {
        cin >> x[i];
    }
    vector<int> nx(n), pr(n);
    for (int i = 0; i < n; i++) {
        int nxv = x[i] + k;
        nx[i] = lower_bound(x.begin(), x.end(), nxv) - x.begin();
        int prv = x[i] - k;
        pr[i] = upper_bound(x.begin(), x.end(), prv) - x.begin() - 1;
        // cout << i << "   " << nx[i] << " " << pr[i] << endl;
    }
    int lg = 18;
    vector<vector<int>> lup(lg, vector<int>(n)), ldw(lg, vector<int>(n)), vup(lg, vector<int>(n)), vdw(lg, vector<int>(n));
    for (int i = 0; i < n; i++) {
        lup[0][i] = nx[i];
        if (lup[0][i] != n) {
            vup[0][i] = nx[i] - 1;
        }
        ldw[0][i] = pr[i];
        if (ldw[0][i] != -1) {
            vdw[0][i] = pr[i];
        }
    }
    for (int i = 1; i < lg; i++) {
        // cout << i << " : ";
        for (int j = 0; j < n; j++) {
            // cout << "(" << lup[i - 1][j] << ", " << vup[i - 1][j] << ")  ";
            if (lup[i - 1][j] == n) {
                lup[i][j] = n;
                continue;
            }
            lup[i][j] = lup[i - 1][lup[i - 1][j]];
            vup[i][j] = vup[i - 1][lup[i - 1][j]] + vup[i - 1][j];
        }
    // cout << ";   ";
        for (int j = 0; j < n; j++) {
            // cout << "(" << ldw[i - 1][j] << ", " << vdw[i - 1][j] << ")  ";
            if (ldw[i - 1][j] == -1) {
                ldw[i][j] = -1;
                continue;
            }
            ldw[i][j] = ldw[i - 1][ldw[i - 1][j]];
            vdw[i][j] = vdw[i - 1][ldw[i - 1][j]] + vdw[i - 1][j];
        }
        // cout << endl;
    }
    int q; cin >> q;
    while (q--) {
        int l, r; cin >> l >> r; l--; r--;
        int val = -l + 1;
        int pos = l;
        for (int i = lg - 1; i >= 0; i--) {
            if (lup[i][pos] <= r) {
                val -= vup[i][pos];
                pos = lup[i][pos];
                // cout << "(" << i << ", " <<  pos << "); ";
            }
        }
        // cout << endl;
        val += r;
        pos = r;
        for (int i = lg - 1; i >= 0; i--) {
            if (ldw[i][pos] >= l) {
                val += vdw[i][pos];
                pos = ldw[i][pos];
                // cout << "(" << i << ", " <<  pos << "); ";
            }
        }
        // cout << endl;
        cout << val << endl;

    }


    return 0;
}