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;

int64_t N, Q, L, R, A[200000], D[200000], X[200000], S[200000], T[200000];

int64_t calc(int64_t v){
    for(int i=0; i<Q; i++){
        if(D[i] == 1 && X[i] <= v) v = T[i]*(v+S[i]);
        if(D[i] == 2 && v <= X[i]) v = (v-S[i])/T[i];
    }
    return v;
}

int main(){
    cin >> N >> Q >> L >> R;
    for(int i=0; i<N; i++) cin >> A[i];
    for(int i=0; i<Q; i++) cin >> D[i] >> X[i] >> S[i] >> T[i];

    int64_t mx = *max_element(A, A+N), mn = *min_element(A, A+N);
    int64_t rok = mn-1, rng = mx+1;
    while(rng-rok>1){
        int64_t mid = (rng+rok)/2;
        (calc(mid) <= R ? rok : rng) = mid;
    }
    int64_t lng = mn-1, lok = mx+1;
    while(lok-lng>1){
        int64_t mid = (lng+lok)/2;
        (calc(mid) >= L ? lok : lng) = mid;
    }
    int ans = 0;
    for(int i=0; i<N; i++) if(lok <= A[i] && A[i] <= rok) ans++;
    cout << ans << endl;
    return 0;
}