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;
using Int = long long;

struct Query {
	Int q, x, s, t;
	Query(){}
};

int main() {
	Int n, q, l, r;
	cin >> n >> q >> l >> r;
	vector<Int> a(n);
	for(auto& x : a) cin >> x;
	sort(a.begin(), a.end());

	vector<Query> query(q);
	for(auto& x : query) {
		cin >> x.q >> x.x >> x.s >> x.t;
	}

	auto sim = [&](Int a) {
		for(auto& x : query) {
			if (x.q == 1) {
				if (a < x.x) continue;
				a += x.s;
				a *= x.t;
			} else {
				if (a > x.x) continue;
				a -= x.s;
				bool neg = (a < 0);
				a = abs(a);
				a /= x.t;
				if (neg) a = -a;
			}
		}
		return a;
	};

	Int lx, rx;
	// finally no less than l (max),
	//     and no more than r (min)
	{
		Int ok = n, ng = -1;
		while (ok - ng > 1) {
			Int mid = (ok + ng) / 2;
			(sim(a[mid]) >= l ? ok : ng) = mid;
		}
		lx = ok;
	}
	if (lx == n) {
		cout << 0 << endl;
		return 0;
	}

	{
		Int ok = -1, ng = n;
		while (ng - ok > 1) {
			Int mid = (ok + ng) / 2;
			(sim(a[mid]) <= r ? ok : ng) = mid;
		}
		rx = ok;
	}
	if (rx == -1) {
		cout << 0 << endl;
		return 0;
	}

	cout << rx - lx + 1 << endl;
	return 0;
}