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 i64 = int64_t;

struct Query{
    i64 q, x, s, t;
};

void update(int idx, vector<i64> &v, deque<bool> &updated, const vector<Query> &query){
    if(updated[idx])return;
    for(auto q: query){
        if(q.q == 1){
            if(v[idx] < q.x)continue;
            v[idx] += q.s;
            v[idx] *= q.t;
        }else{
            if(v[idx] > q.x)continue;
            v[idx] -= q.s;
            v[idx] /= q.t;
        }
    }
    updated[idx] = true;
}

int main(){
    i64 n, q, l, r;
    cin >> n >> q >> l >> r;
    vector<i64> v;
    for(int i=0;i<n;++i){
        i64 a;
        cin >> a;
        v.push_back(a);
    }
    sort(v.begin(), v.end());
    deque<bool> updated(n, false);

    vector<Query> query;
    for(int i=0;i<q;++i){
        i64 q, x, s, t;
        cin >> q >> x >> s >> t;
        query.push_back({q, x, s, t});
    }

    int ri = n, li = -1;
    while(ri-li > 1){
        int mi = (ri + li) / 2;
        update(mi, v, updated, query);
        if(v[mi] > r)ri = mi;
        else li = mi;
    }
    int R = ri;
    ri = n; li = -1;
    while(ri-li > 1){
        int mi = (ri + li) / 2;
        update(mi, v, updated, query);
        if(v[mi] < l)li = mi;
        else ri = mi;
    }
    int L = li + 1;

    cout << R - L << endl;

    return 0;
}