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 pb push_back
#define mp make_pair
#define fi first
#define se second

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

template <typename T> bool chkmax(T &x,T y){return x<y?x=y,true:false;}
template <typename T> bool chkmin(T &x,T y){return x>y?x=y,true:false;}

ll readint(){
	ll x=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}

const ll inf=(1ull<<63)-1;
ll n,q,l,r;
ll a[200005],opt[200005],X[200005],S[200005],T[200005];

int main(){
	n=readint(); q=readint(); l=readint(); r=readint();
	for(int i=1;i<=n;i++) a[i]=readint();
	for(int i=1;i<=q;i++){
		opt[i]=readint(); X[i]=readint(); S[i]=readint(); T[i]=readint();
	}
	for(int i=q;i>=1;i--){
		ll s=S[i],t=T[i],x=X[i];
		if(opt[i]==1){
			ll tl=l/t-s,tr=r/t-s;
			if(l>x) l=max(tl,x),r=max(tr,x-1);
			else if(r<x);
			else r=max(tr,x-1);
		}
		else{
			ll tl,tr;
			if(l<0){
				if(-inf/(l-1)<=t) tl=-inf;
				else tl=t*(l-1)+s+1;
			}
			else{
				if((inf-s)/l<=t) tl=inf;
				else tl=t*l+s;
			}
			if(r<0){
				if(-inf/r<=t) tr=-inf;
				else tr=t*r+s;
			}
			else{
				if((inf-s+1)/(r+1)<=t) tr=inf;
				else tr=t*(r+1)+s-1;
			}
			if(l>x);
			else if(r<x) l=min(tl,x+1),r=min(tr,x);
			else l=min(tl,x+1);
		}
//		cout<<"test "<<i<<' '<<l<<' '<<r<<endl;
		if(l>r) return printf("0\n"),0;
	}
	int cnt=0;
//	cout<<"end "<<l<<' '<<r<<endl;
//	for(int i=1;i<=n;i++) cout<<a[i]<<' ';
//	cout<<endl;
	for(int i=1;i<=n;i++) if(l<=a[i]&&a[i]<=r) cnt++;
	printf("%d\n",cnt);
	return 0;
}