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;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define fi first
#define se second
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
const ll mod=1000000007;
ll powmod(ll a,ll b) {ll res=1;a%=mod;for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
// head

const int N=201000;
int n,q,a[N];
ll L,R,f[N][4];
int main() {
	scanf("%d%d%lld%lld",&n,&q,&L,&R);
	rep(i,0,n) scanf("%d",a+i);
	rep(i,0,q) scanf("%lld%lld%lld%lld",f[i],f[i]+1,f[i]+2,f[i]+3);
	sort(a,a+n);
	int l=-1,r=n;
	while (l+1<r) {
		int md=(l+r)>>1;
		__int128_t p=a[md];
		rep(i,0,q) {
			if (f[i][0]==1) {
				if (p>=f[i][1]) p=(p+f[i][2])*f[i][3];
			} else {
				if (p<=f[i][1]) p=(p-f[i][2])/f[i][3];
			}
		}
		//printf("%d %lld\n",md,(ll)p);
		if (p>=L) r=md; else l=md;
	}
	int x=r;
	l=-1,r=n;
	while (l+1<r) {
		int md=(l+r)>>1;
		__int128_t p=a[md];
		rep(i,0,q) {
			if (f[i][0]==1) {
				if (p>=f[i][1]) p=(p+f[i][2])*f[i][3];
			} else {
				if (p<=f[i][1]) p=(p-f[i][2])/f[i][3];
			}
		}
		//printf("%d %lld\n",md,(ll)p);
		if (p<=R) l=md; else r=md;
	}
	//printf("%d %d\n",l,x);
	printf("%d\n",l-x+1);
}