Problem: — Willem...

— What's the matter?

— It seems that there's something wrong with Seniorious...

— I'll have a look...

<image>

Seniorious is made by linking special talismans in particular order.

After over 500 years, the carillon is now in bad condition, so Willem decides to examine it thoroughly.

Seniorious has n pieces of talisman. Willem puts them in a line, the i-th of which is an integer ai.

In order to maintain it, Willem needs to perform m operations.

There are four types of operations:

  * 1 l r x: For each i such that l ≤ i ≤ r, assign ai + x to ai.
  * 2 l r x: For each i such that l ≤ i ≤ r, assign x to ai.
  * 3 l r x: Print the x-th smallest number in the index range [l, r], i.e. the element at the x-th position if all the elements ai such that l ≤ i ≤ r are taken and sorted into an array of non-decreasing integers. It's guaranteed that 1 ≤ x ≤ r - l + 1.
  * 4 l r x y: Print the sum of the x-th power of ai such that l ≤ i ≤ r, modulo y, i.e. <image>.

Input

The only line contains four integers n, m, seed, vmax (1 ≤ n, m ≤ 105, 0 ≤ seed < 109 + 7, 1 ≤ vmax ≤ 109).

The initial values and operations are generated using following pseudo code:
    
    
      
    def rnd():  
      
        ret = seed  
        seed = (seed * 7 + 13) mod 1000000007  
        return ret  
      
    for i = 1 to n:  
      
        a[i] = (rnd() mod vmax) + 1  
      
    for i = 1 to m:  
      
        op = (rnd() mod 4) + 1  
        l = (rnd() mod n) + 1  
        r = (rnd() mod n) + 1  
      
        if (l > r):   
             swap(l, r)  
      
        if (op == 3):  
            x = (rnd() mod (r - l + 1)) + 1  
        else:  
            x = (rnd() mod vmax) + 1  
      
        if (op == 4):  
            y = (rnd() mod vmax) + 1  
      
    

Here op is the type of the operation mentioned in the legend.

Output

For each operation of types 3 or 4, output a line containing the answer.

Examples

Input

10 10 7 9


Output

2
1
0
3


Input

10 10 9 9


Output

1
1
3
3

Note

In the first example, the initial array is {8, 9, 7, 2, 3, 1, 5, 6, 4, 8}.

The operations are:

  * 2 6 7 9
  * 1 3 10 8
  * 4 4 6 2 4
  * 1 4 5 8
  * 2 1 7 1
  * 4 7 9 4 4
  * 1 2 7 9
  * 4 5 8 1 1
  * 2 5 7 5
  * 4 3 10 8 5

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<int> ds;
vector<vector<pair<int, int> > > es;
vector<bool> bolo;
vector<pair<int, int> > dynamic_minu_ones;
vector<int> pocet_hran;
vector<int> to_remove;
int n, m;
bool da_sa = true;
long long PRIME = 1e9 + 7;
long long fakt[1000000 + 7];
long long inv_a[1000000 + 7];
long long seed, op, l, r, x, y, vmax;
long long rnd() {
  long long ret = seed;
  seed = (seed * 7 + 13) % 1000000007;
  return ret;
}
void generate_cmd() {
  op = (rnd() % 4) + 1;
  l = (rnd() % n) + 1;
  r = (rnd() % n) + 1;
  if (l > r) swap(l, r);
  if (op == 3)
    x = (rnd() % (r - l + 1)) + 1;
  else
    x = (rnd() % vmax) + 1;
  if (op == 4) y = (rnd() % vmax) + 1;
}
struct Entry {
  long long pos;
  long long val;
};
bool operator<(const Entry& x, const Entry& y) {
  return std::tie(x.pos, x.val) < std::tie(y.pos, y.val);
}
set<Entry>::iterator find_iterator(long long pos, set<Entry>& arr) {
  Entry en = {pos, 0};
  auto it = arr.lower_bound(en);
  if (it->pos > pos) {
    it--;
    auto it_val = *it;
    Entry en = {pos, it_val.val};
    it = arr.insert(en).first;
  }
  return it;
}
long long power(long long x, long long m, long long prv) {
  long long res = 1;
  long long moc = x;
  moc %= prv;
  while (m) {
    if (m % 2 == 1) {
      res *= moc;
      res %= prv;
    }
    moc *= moc;
    moc %= prv;
    m /= 2;
  }
  return res;
}
int main() {
  cin >> n >> m >> seed >> vmax;
  set<Entry> arr;
  for (long long i = 1; i <= n; i++) {
    Entry en = {i, (rnd() % vmax) + 1};
    arr.insert(en);
  }
  Entry en = {n + 1, -1};
  arr.insert(en);
  for (int i = 0; i < (m); i++) {
    generate_cmd();
    auto it_l = find_iterator(l, arr);
    auto it_r = find_iterator(r + 1, arr);
    auto it_c = it_l;
    if (op == 1) {
      while (it_l != it_r) {
        it_c++;
        auto it_val = *it_l;
        arr.erase(it_l);
        Entry en = {it_val.pos, it_val.val + x};
        arr.insert(en);
        it_l = it_c;
      }
    } else if (op == 2) {
      while (it_l != it_r) {
        it_c++;
        arr.erase(it_l);
        it_l = it_c;
      }
      Entry en = {l, x};
      arr.insert(en);
    } else if (op == 3) {
      multiset<pair<long long, long long> > mn;
      while (it_l != it_r) {
        it_c++;
        mn.insert(make_pair(it_l->val, it_c->pos - it_l->pos));
        it_l = it_c;
      }
      for (auto p : mn) {
        if (x <= p.second) {
          cout << p.first << endl;
          break;
        }
        x -= p.second;
      }
    } else if (op == 4) {
      do {
        if (0)
          std::cerr << "op4"
                    << " ";
      } while (0);
      long long res = 0;
      do {
        if (0)
          std::cerr << "l"
                    << ": " << l << std::endl;
      } while (0);
      do {
        if (0)
          std::cerr << "r"
                    << ": " << r << std::endl;
      } while (0);
      do {
        if (0)
          std::cerr << "x"
                    << ": " << x << std::endl;
      } while (0);
      do {
        if (0)
          std::cerr << "y"
                    << ": " << y << std::endl;
      } while (0);
      do {
        if (0)
          std::cerr << "x"
                    << ": " << x << std::endl;
      } while (0);
      while (it_l != it_r) {
        it_c++;
        do {
          if (0)
            std::cerr << "it_c->pos"
                      << ": " << it_c->pos << std::endl;
        } while (0);
        do {
          if (0)
            std::cerr << "it_l->pos"
                      << ": " << it_l->pos << std::endl;
        } while (0);
        do {
          if (0)
            std::cerr << "it_c->pos - it_l->pos"
                      << ": " << it_c->pos - it_l->pos << std::endl;
        } while (0);
        res += ((it_c->pos - it_l->pos) * power(it_l->val, x, y)) % y;
        res %= y;
        it_l = it_c;
      }
      cout << res << endl;
    }
  }
}