Problem: B: AddMulSubDiv

Problem Statement

You have an array A of N integers. A_i denotes the i-th element of A.

You have to process one of the following queries Q times:

* Query 1: The query consists of non-negative integer x, and two positive integers s, t. For all the elements greater than or equal to x in A, you have to add s to the elements, and then multiply them by t. That is, an element with v (v \geq x) becomes t(v + s) after this query.


* Query 2: The query consists of non-negative integer x, and two positive integers s, t. For all the elements less than or equal to x in A, you have to subtract s from the elements, and then divide them by t. If the result is not an integer, you truncate it towards zero. That is, an element with v (v \leq x) becomes $\mathrm{trunc}$ ( \frac{v - s}{t} ) after this query, where $\mathrm{trunc}$ ( y ) is the integer obtained by truncating y towards zero.


* "Truncating towards zero" means converting a decimal number to an integer so that if x = 0.0 then 0 , otherwise an integer whose absolute value is the maximum integer no more than |x| and whose sign is same as x. For example, truncating 3.5 towards zero is 3, and truncating -2.8 towards zero is -2.



After applying Q queries one by one, how many elements in A are no less than L and no more than R?

Input


N Q L R
A_1 A_2 ... A_N
q_1 x_1 s_1 t_1
:
q_Q x_Q s_Q t_Q


* The first line contains four integers N, Q, L, and R. N is the number of elements in an integer array A, Q is the number of queries, and L and R specify the range of integers you want to count within after the queries.
* The second line consists of N integers, the i-th of which is the i-th element of A.
* The following Q lines represent information of queries. The j-th line of them corresponds to the j-th query and consists of four integers q_j, x_j, s_j, and t_j. Here, q_j = 1 stands for the j-th query is Query 1, and q_j = 2 stands for the j-th query is Query 2. x_j, s_j, and t_j are parameters used for the j-th query.



Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq Q \leq 2 \times 10^5
* -2^{63} < L \leq R < 2^{63}
* 0 \leq |A_i| \leq 10^9
* q_j \in \\{ 1, 2 \\}
* 0 \leq x_j < 2^{63}
* 1 \leq s_j, t_j \leq 10^9
* Inputs consist only of integers.
* The absolute value of any element in the array dosen't exceed 2^{63} at any point during query processing.



Output

Output the number of elements in A that are no less than L and no more than R after processing all given queries in one line.

Sample Input 1


3 3 3 10
1 -2 3
1 2 2 3
2 20 1 3
2 1 20 5


Output for Sample Input 1


1





Example

Input

3 3 3 10
1 -2 3
1 2 2 3
2 20 1 3
2 1 20 5


Output

1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define REP(i, N) for (ll i = 0; i < (N); ++i)

ll N, Q, L, R;
vector<ll> A;
vector<tuple<ll, ll, ll, ll>> query;

const ll INF = (ll)1e9 + 7;

signed main() {

    cin >> N >> Q >> L >> R;

    A.resize(N + 1);
    A[0] = -INF;
    REP(i, N) cin >> A[i + 1];

    sort(A.begin(), A.end());

    // REP(i, N) cerr << A[i] << endl;

    REP(i, Q) {
        ll q, x, s, t;
        cin >> q >> x >> s >> t;
        query.emplace_back(make_tuple(q, x, s, t));
    }

    function<bool(ll, ll)> check = [&](ll m, ll MAX) {
        if (m == -INF) return true;
        REP(i, Q) {
            ll q, x, s, t;
            tie(q, x, s, t) = query[i];
            if (q == 1) {
                if (m >= x) {
                    m = t * (m + s);
                }
            } else {
                if (m <= x) {
                    m = (m - s) / t;
                }
            }
        }
        return (m <= MAX);
    };

    ll l = 0, r = 0;

    {
        ll ok = 0, ng = N + 1;
        while (abs(ok - ng) > 1) {
            ll mid = (ok + ng) / 2;
            if (check(A[mid], R)) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        r = ok;
    }

    {
        ll ok = 0, ng = N + 1;
        while (abs(ok - ng) > 1) {
            ll mid = (ok + ng) / 2;
            if (check(A[mid], L - 1)) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        l = ok;
    }

    cout << max<ll>(0, r - l) << endl;

    // cerr << l << ' ' << r << endl;

}