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 ll = long long int;

struct Query{
    int type;
    long long int x,s,t;
    Query(const int ty,const long long int xx,const long long int ss,const long long int tt){
        type=ty;
        x=xx,s=ss,t=tt;
    }
};

int main() {
    int N,Q;
    long long int L,R;
    cin>>N>>Q>>L>>R;
    vector<long long int>v(N);
    for(auto &i:v)cin>>i;
    //v.push_back(1LL<<63);
    //cout<<(1LL<<63)<<endl;
    sort(v.begin(),v.end());
    vector<Query>q;
    for(int i=0;i<Q;i++){
        long long int a,b,c,d;
        cin>>a>>b>>c>>d;
        q.push_back(Query(a,b,c,d));
    }
    //cout<<"hoge"<<endl;
    int Lindex=0;
    int l=-1,r=v.size();
    while(r-l>1){
        int mid=(l+r)/2;
       //cout<<l<<" "<<r<<endl;
        long long int num=v[mid];
        for(auto i:q){
                if(i.type==1){
                    if(i.x<=num){
                        num+=i.s;
                        num*=i.t;
                    }
                }
                else {
                    if(i.x>=num){
                        num-=i.s;
                        if(num)num=(abs(num)/i.t)*(num/abs(num));
                    }
                }
        }
        if(num>=L)r=mid;
        else l=mid;
    }
    Lindex=l;
    l=-1,r=v.size();
    int Rindex=0;
    while(r-l>1){
        int mid=(l+r)/2;
        long long int num=v[mid];
        for(auto i:q){
                if(i.type==1){
                    if(i.x<=num){
                        num+=i.s;
                        num*=i.t;
                    }
                }
                else {
                    if(i.x>=num){
                        num-=i.s;
                        if(num)num=(abs(num)/i.t)*(num/abs(num));
                    }
                }
        }
        //cout<<mid<<" "<<num<<endl;
        if(num>R)r=mid;
        else l=mid;
    }
    Rindex=l;
    //cout<<Rindex<<" "<<Lindex<<endl;
    cout<<Rindex-Lindex<<endl;
    return 0;
}