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:
// untiioiiiiiiiiiiiiiasaaa
#include<bits/stdc++.h>
using namespace std;
#define X first
#define S second

#define all(v) (v).begin(), (v).end()
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,b) FOR(i,0,b)
#define reps FOR
#define eb emplace_back
#define pb eb

using LL = long long;
using pii = pair<int, int>;

int N;
int Q;
LL L, R;
vector<LL> as;
LL cmd[214514][4];

LL Eval(LL v) {
  rep(i, Q) {
    if (cmd[i][0] == 1) {
      if (cmd[i][1] <= v) {
        v = (v+cmd[i][2])*cmd[i][3];
      }
    } else if (cmd[i][0] == 2) {
      if (cmd[i][1] >= v) {
        v = (v-cmd[i][2])/cmd[i][3];
      }
    }
  }
  return v;
}

int main() {
  cin >> N >> Q >> L >> R;
  rep(i, N) {
    LL a;
    cin >> a;
    as.eb(a);
  }
  sort(all(as));

  rep(i, Q) {
    rep(j, 4) {
      cin >> cmd[i][j];
    }
  }

  int ans = 0;
  {
    int low = -1;
    int high = N;
    while (high - low > 1) {
      int mid = (high+low)/2;
      LL res = Eval(as[mid]);
      if (L > res) low = mid;
      else high = mid;
    }
    ans -= low;
  }
  {
    int low = -1;
    int high = N;
    while (high - low > 1) {
      int mid = (high+low)/2;
      LL res = Eval(as[mid]);
      if (R >= res) low = mid;
      else high = mid;
    }
    ans += low;
  }
  cout << ans << endl;
}