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 <cstdio>
#include <algorithm>

const int maxn=2e5+5;
#define int long long
struct question{
	int opt,x,s,t;
}q[maxn];

int n,Q,L,R,a[maxn];

#define F_L 1
#define F_R 0

inline bool check(int x,bool flag){
	for(int i=1;i<=Q;i++){
		if(q[i].opt==1){
			if(x>=q[i].x){
			x+=q[i].s;x*=q[i].t;}
		}else{
			if(x<=q[i].x){
			x-=q[i].s;x/=q[i].t;}
		}
	}
	//printf("%d\n",x);
	if(flag){
		return x>=L;
	}return x<=R;
}

signed main(){
	scanf("%lld%lld%lld%lld",&n,&Q,&L,&R);
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
	std::sort(a+1,a+n+1);
	for(int i=1;i<=Q;i++) scanf("%lld%lld%lld%lld",&q[i].opt,&q[i].x,&q[i].s,&q[i].t);
	int l=1,r=n,mid,res=0;
	while(l<=r){
		mid=(l+r)>>1;
		int now=a[mid];
		if(check(now,F_L)){
			r=mid-1;
			res=mid;
		}else l=mid+1;
		//printf("%d\n",mid);
	}int ansl=res;
	l=1,r=n,res=0;//printf("------------------\n");
	while(l<=r){
		mid=(l+r)>>1;
		int now=a[mid];
		if(check(now,F_R)){
			l=mid+1;
			res=mid;
		}else r=mid-1;
		//printf("%d\n",mid);
	}
	//printf("%lld %lld\n",ansl,res);
	printf("%lld\n",res-ansl+1);
	return 0;
}