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 <iostream>
#include <vector>
#include <algorithm>
#include <tuple>
#include <array>

#define ll long long

using namespace std;

vector<ll> A;
vector<array<long long, 4>> Q;

ll calc(ll v) {
	for (const auto& q : Q) {
		ll p, x, s, t;
		p = q[0];
		x = q[1];
		s = q[2];
		t = q[3];

		if (p == 1 and v >= x) {
			v = t * (v + s);
		}
		else if (p == 2 and v <= x) {
			v = (v - s) / t;
		}

	}

	return v;
}

signed main() {
	int n, q;
	ll L, R;
	cin >> n >> q >> L >> R;

	A.resize(n);
	for (auto& a : A) cin >> a;
	sort(A.begin(), A.end());

	for (int i = 0; i < q; i++) {
		ll p, x, s, t;
		cin >> p >> x >> s >> t;
		Q.push_back({ p, x, s, t });
	}

	int ng = -1, ok = n;

	while (ok - ng > 1) {
		int mid = (ok + ng) / 2;
		if (calc(A[mid]) >= L) {
			ok = mid;
		}
		else {
			ng = mid;
		}
	}

	int l = ok;

	ng = n, ok = -1;

	while (abs(ok - ng) > 1) {
		int mid = (ok + ng) / 2;
		if (calc(A[mid]) <= R) {
			ok = mid;
		}
		else {
			ng = mid;
		}
	}

	int r = ok;
	
	cout << max(0, r - l + 1) << endl;

}