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 n, m, seed, vmax;
long long rnd() {
  long long res = seed;
  seed = (seed * 7ll + 13ll) % 1000000007ll;
  return res;
}
long long zzpow(long long x, long long p, long long mod) {
  if (!p) return 1ll;
  long long t = zzpow(x, p / 2, mod);
  if (p % 2) return t * t % mod * (x % mod) % mod;
  return t * t % mod;
}
long long a[100005];
long long b[100005];
set<pair<pair<long long, long long>, long long> > arr;
void checkSame() {
  for (int i = 1; i <= n; i++) {
    cout << a[i] << ' ';
  }
  cout << endl;
  for (auto v : arr) {
    for (int i = v.first.first; i <= v.first.second; i++) b[i] = v.second;
  }
  for (int i = 1; i <= n; i++) {
    cout << b[i] << ' ';
  }
  cout << endl;
  for (int i = 1; i <= n; i++) {
    if (a[i] != b[i]) exit(0);
  }
}
int main() {
  cin >> n >> m >> seed >> vmax;
  for (int i = 1; i <= n; i++)
    a[i] = rnd() % vmax + 1,
    arr.insert(pair<pair<long long, long long>, long long>(
        pair<long long, long long>(i, i), a[i]));
  for (int _ = 1; _ <= m; _++) {
    long long op = (rnd() % 4) + 1;
    long long L = (rnd() % n) + 1;
    long long R = (rnd() % n) + 1;
    if (L > R) swap(L, R);
    long long x = -1, y = -1;
    if (op == 3)
      x = (rnd() % (R - L + 1)) + 1;
    else
      x = (rnd() % vmax) + 1;
    if (op == 4) y = (rnd() % vmax) + 1;
    vector<pair<pair<long long, long long>, long long> > lst;
    while (arr.size()) {
      set<pair<pair<long long, long long>, long long> >::iterator it =
          arr.lower_bound(pair<pair<long long, long long>, long long>(
              pair<long long, long long>(L, 0), 0));
      if (it == arr.end() || R < (*it).first.first) {
        if (it == arr.begin())
          break;
        else {
          it--;
          pair<pair<long long, long long>, long long> cur = *it;
          if (cur.first.second < L) break;
          arr.erase(it);
          pair<pair<long long, long long>, long long> upd =
              pair<pair<long long, long long>, long long>(
                  pair<long long, long long>(L, cur.first.second), cur.second);
          pair<pair<long long, long long>, long long> remain =
              pair<pair<long long, long long>, long long>(
                  pair<long long, long long>(cur.first.first, L - 1),
                  cur.second);
          if (remain.first.first <= remain.first.second) arr.insert(remain);
          if (upd.first.second > R) {
            remain.first.first = R + 1;
            remain.first.second = upd.first.second;
            upd.first.second = R;
            if (remain.first.first <= remain.first.second) arr.insert(remain);
          }
          lst.push_back(upd);
        }
      } else {
        if ((*it).first.second <= R) {
          lst.push_back(*it);
          arr.erase(it);
        } else {
          pair<pair<long long, long long>, long long> cur = *it;
          arr.erase(it);
          pair<pair<long long, long long>, long long> upd =
              pair<pair<long long, long long>, long long>(
                  pair<long long, long long>(cur.first.first, R), cur.second);
          pair<pair<long long, long long>, long long> remain =
              pair<pair<long long, long long>, long long>(
                  pair<long long, long long>(R + 1, cur.first.second),
                  cur.second);
          lst.push_back(upd);
          if (remain.first.first <= remain.first.second) arr.insert(remain);
        }
      }
    }
    if (op == 1) {
      for (auto v : lst)
        arr.insert(
            pair<pair<long long, long long>, long long>(v.first, v.second + x));
      continue;
    }
    if (op == 2) {
      arr.insert(pair<pair<long long, long long>, long long>(
          pair<long long, long long>(L, R), x));
      continue;
    }
    if (op == 3) {
      sort(lst.begin(), lst.end(),
           [](pair<pair<long long, long long>, long long> xx,
              pair<pair<long long, long long>, long long> yy) {
             return xx.second < yy.second;
           });
      long long cnt = 0;
      for (auto v : lst) {
        cnt += v.first.second - v.first.first + 1;
        if (x <= cnt) {
          cout << v.second << '\n';
          break;
        }
      }
      for (auto v : lst) arr.insert(v);
      continue;
    }
    if (op == 4) {
      long long res = 0;
      for (auto v : lst)
        res = (res +
               zzpow(v.second, x, y) * (v.first.second - v.first.first + 1)) %
              y;
      for (auto v : lst) arr.insert(v);
      cout << res << '\n';
      continue;
    }
    assert(0);
  }
}