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 seed;
inline long long rnd() {
  long long rt = seed;
  seed = (7ll * seed + 13) % 1000000007;
  return rt;
}
struct seg {
  long long l, r, val;
  bool operator<(const seg &r) const { return l < r.l; }
};
set<seg> st;
long long pw(long long b, long long n, long long m, long long a = 1) {
  while (n) {
    if (n & 1) a = a * b % m;
    b = b * b % m;
    n >>= 1;
  }
  return a;
}
int32_t main() {
  long long n, m, V;
  cin >> n >> m >> seed >> V;
  for (long long i = 1; i <= n; ++i) {
    st.insert({i, i, rnd() % V + 1});
  }
  long long op, l, r, x, y;
  long long lineoutput = 0;
  for (long long i = 1; i <= m; ++i) {
    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() % V + 1;
    if (op == 4) y = rnd() % V + 1;
    if (op == 1) {
      while (l <= r) {
        auto it = st.upper_bound(seg{l, l, 0});
        --it;
        auto tk = *it;
        st.erase(it);
        if (tk.l < l) {
          auto ano = tk;
          ano.r = l - 1;
          st.insert(ano);
          tk.l = l;
        }
        if (tk.r > r) {
          auto ano = tk;
          ano.l = r + 1;
          st.insert(ano);
          tk.r = r;
        }
        tk.val += x;
        st.insert(tk);
        l = tk.r + 1;
      }
    } else if (op == 2) {
      long long zzl = l;
      while (l <= r) {
        auto it = st.upper_bound(seg{l, l, 0});
        --it;
        auto tk = *it;
        st.erase(it);
        if (tk.l < l) {
          auto ano = tk;
          ano.r = l - 1;
          st.insert(ano);
          tk.l = l;
        }
        if (tk.r > r) {
          auto ano = tk;
          ano.l = r + 1;
          st.insert(ano);
          tk.r = r;
        }
        l = tk.r + 1;
      }
      st.insert(seg{zzl, r, x});
    } else if (op == 3) {
      multiset<pair<long long, long long>> stt;
      while (l <= r) {
        auto it = st.upper_bound(seg{l, l, 0});
        --it;
        auto tk = *it;
        st.erase(it);
        if (tk.l < l) {
          auto ano = tk;
          ano.r = l - 1;
          st.insert(ano);
          tk.l = l;
        }
        if (tk.r > r) {
          auto ano = tk;
          ano.l = r + 1;
          st.insert(ano);
          tk.r = r;
        }
        st.insert(tk);
        stt.insert(pair<long long, long long>(tk.val, tk.r - tk.l + 1));
        l = tk.r + 1;
      }
      long long lay = 0;
      for (pair<long long, long long> p : stt) {
        if (lay + p.second >= x) {
          cout << p.first << '\n';
          break;
        } else
          lay += p.second;
      }
      ++lineoutput;
    } else {
      long long out = 0;
      while (l <= r) {
        auto it = st.upper_bound(seg{l, l, 0});
        --it;
        auto tk = *it;
        st.erase(it);
        if (tk.l < l) {
          auto ano = tk;
          ano.r = l - 1;
          st.insert(ano);
          tk.l = l;
        }
        if (tk.r > r) {
          auto ano = tk;
          ano.l = r + 1;
          st.insert(ano);
          tk.r = r;
        }
        st.insert(tk);
        out += (tk.r - tk.l + 1) * pw(tk.val % y, x, y) % y;
        l = tk.r + 1;
      }
      cout << out % y << '\n';
      ++lineoutput;
    }
  }
}