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;
long long POW(long long base, long long ex, long long mod) {
  if (ex == 0) return 1;
  if (ex == 1) return base % mod;
  long long res = POW(base, ex / 2, mod);
  res = (res * res) % mod;
  if (ex % 2 == 1) res = (res * (base % mod)) % mod;
  return res;
}
long long seed, vmax;
long long rnd() {
  long long ans = seed;
  seed = (seed * 7ll + 13ll) % 1000000007ll;
  return ans;
}
map<long long, long long> tree;
map<long long, long long>::iterator search(int x) {
  map<long long, long long>::iterator it = tree.upper_bound(x);
  it--;
  if (it->first != x) {
    tree[x] = it->second;
    it = tree.lower_bound(x);
  }
  return it;
}
void add(int l, int r, long long x) {
  for (map<long long, long long>::iterator L = search(l), R = search(r), i = L;
       i != R; i++)
    i->second += x;
}
void replace(int l, int r, long long x) {
  map<long long, long long>::iterator L = search(l), R = search(r);
  L->second = x;
  ++L;
  for (map<long long, long long>::iterator i = L; i != R; i = L) {
    ++L;
    tree.erase(i);
  }
}
long long Xth_small(int l, int r, int x) {
  vector<pair<long long, int>> aux;
  for (map<long long, long long>::iterator L = search(l), R = search(r), i = L;
       i != R; i++) {
    map<long long, long long>::iterator r = i;
    r++;
    aux.push_back(make_pair(i->second, r->first - i->first));
  }
  sort(aux.begin(), aux.end());
  x--;
  for (auto movil : aux) {
    if (x < movil.second) return movil.first;
    x -= movil.second;
  }
  return aux[-1].second;
}
long long sum(int l, int r, long long ex, long long mod) {
  long long res = 0;
  for (map<long long, long long>::iterator L = search(l), R = search(r), i = L;
       i != R; i++) {
    map<long long, long long>::iterator r = i;
    r++;
    long long aux = (r->first - i->first);
    aux *= POW(i->second, ex, mod);
    aux = aux % mod;
    res = (res + aux) % mod;
  }
  return res;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m, s = -1;
  cin >> n >> m >> seed >> vmax;
  for (int i = 0; i < n; i++) {
    int x = (rnd() % vmax) + 1;
    if (x == s) continue;
    tree[i] = x;
    x = s;
  }
  tree[n] = rand() % rand() % rand() % rand() % rand() % rand() % rand() %
            rand() % rand() % rand() % rand() % rand() % rand();
  for (int i = 0; i < m; i++) {
    int t = 1 + (rnd() % 4), l = rnd() % n, r = rnd() % n;
    if (l > r) swap(l, r);
    ++r;
    if (t == 1) {
      int x = 1 + (rnd() % vmax);
      add(l, r, x);
    } else if (t == 2) {
      int x = 1 + (rnd() % vmax);
      replace(l, r, x);
    } else if (t == 3) {
      int x = 1 + (rnd() % (r - l));
      cout << Xth_small(l, r, x) << endl;
    } else {
      int x = 1 + (rnd() % vmax), y = 1 + (rnd() % vmax);
      cout << sum(l, r, x, y) << endl;
    }
  }
  return 0;
}