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>
#define int long long
using namespace std;
const int maxn=1000005;
int a[maxn],b[maxn],opt[maxn],limit[maxn],x[maxn],y[maxn],L,R,n,m;
int check(int mid)
{
//	cout<<mid<<" "<<a[mid]<<" ";
	int now=a[mid];
	for(int i=1;i<=m;i++)
	{
		if(opt[i]==1)
		{
			if(now>=limit[i])now=(now+x[i])*y[i];
		}
		else if(now<=limit[i])now=(now-x[i])/y[i];	
	}
	
//	cout<<now<<endl;
	return now;
}
signed main()
{
	cin>>n>>m>>L>>R;
	for(int i=1;i<=n;i++)cin>>a[i];
	for(int i=1;i<=m;i++)cin>>opt[i]>>limit[i]>>x[i]>>y[i];
	sort(a+1,a+1+n);
	int l=1,r=n,ans1=0;
	while(l<=r)
	{
		int mid=(l+r)/2;
		if(check(mid)<=R)ans1=mid,l=mid+1;
		else r=mid-1; 
	} 
//	cout<<ans1<<endl;
	l=1,r=n;int ans2=n+1;
	while(l<=r)
	{
		int mid=(l+r)/2;
		if(check(mid)>=L)ans2=mid,r=mid-1;
		else l=mid+1; 
	} //cout<<ans2<<endl;
	cout<<ans1-ans2+1<<endl;
	
}
/*
3 3 3 10
1 -2 3
1 2 2 3
2 20 1 3
2 1 20 5
首先那些不构成约束的边直接就是2^k/2，随便取，然后有一半的概率是不合法的
对于有约束的边就看下约束
每次枚举一个点，然后开始检查所有边 
 
 */