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;
typedef long long ll;
ll N, Q, L, R;
ll A[200500];
ll q[205000], x[200500], s[200050], t[200050];

ll f(ll now) {
    for(int i = 1; i <= Q; i++) {
        if(q[i] == 1) {
            if(now >= x[i]) {
                now = t[i] * (now + s[i]);
            }
        } else {
            if(now <= x[i]) {
                now = (now - s[i]) / t[i];
            }
        }
    }
    return now;
}

int main() {
    cin >> N >> Q >> L >> R;
    for(int i = 1; i <= N; i++) cin >> A[i];
    for(int i = 1; i <= Q; i++) {
        cin >> q[i] >> x[i] >> s[i] >> t[i];
    }
    ll overok = 1e9+1;
    ll overng = -1e9-1;
    ll underok = -1e9-1;
    ll underng = 1e9+1;
    while(overok - overng > 1) {
        ll mid = (overok + overng) / 2;
        ll tmp = f(mid);
        if(tmp > R) overok = mid;
        else overng = mid;
    }
    while(underng - underok > 1) {
        ll mid = (underok + underng) / 2;
        ll tmp = f(mid);
        if(tmp < L) underok = mid;
        else underng = mid;
    }
    //cerr << overok << " " << underok << endl;
//    cerr << f(overok) << " " << f(overng) << endl;
//    cerr << f(underok) << " " << f(underng) << endl;
    ll ans = 0;
    for(int i = 1; i <= N; i++) {
        if(A[i] < overok && A[i] > underok) {
            ans++;
            //cerr << i << endl;
        }
        //cerr << f(A[i]) << endl;
    }
    cout << ans << endl;
}