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 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 % m;
}
struct meow {
  long long l, r, v;
};
bool operator<(const meow &a, const meow &b) {
  return tie(a.l, a.r, a.v) < tie(b.l, b.r, b.v);
}
long long a[100005];
int32_t main() {
  long long n, m;
  long long seed, vmax;
  cin >> n >> m >> seed >> vmax;
  auto rand = [&]() {
    long long rt = seed;
    seed = (seed * 7 + 13) % 1000000007;
    return rt;
  };
  for (long long i = 1; i <= n; ++i) a[i] = rand() % vmax + 1;
  set<meow> st;
  for (long long i = 1, j; i <= n; i = j) {
    for (j = i + 1; j <= n && a[j] == a[i]; ++j)
      ;
    st.insert({i, j - 1, a[i]});
  }
  for (long long i = 1; i <= m; ++i) {
    long long op = rand() % 4 + 1;
    long long l = rand() % n + 1, r = rand() % n + 1;
    if (l > r) swap(l, r);
    if (op == 1) {
      long long x = rand() % vmax + 1;
      while (l <= r) {
        auto it = st.upper_bound({l, n + 1, 0});
        --it;
        auto p = *it;
        st.erase(it);
        if (p.l < l) {
          auto cp = p;
          cp.r = l - 1;
          st.insert(cp);
          p.l = l;
        }
        if (p.r > r) {
          auto cp = p;
          cp.l = r + 1;
          st.insert(cp);
          p.r = r;
        }
        p.v += x;
        st.insert(p);
        l = p.r + 1;
      }
    } else if (op == 2) {
      long long x = rand() % vmax + 1;
      long long L = l;
      while (l <= r) {
        auto it = st.upper_bound({l, n + 1, 0});
        --it;
        auto p = *it;
        st.erase(it);
        if (p.l < l) {
          auto cp = p;
          cp.r = l - 1;
          st.insert(cp);
          p.l = l;
        }
        if (p.r > r) {
          auto cp = p;
          cp.l = r + 1;
          st.insert(cp);
          p.r = r;
        }
        l = p.r + 1;
      }
      st.insert({L, r, x});
    } else if (op == 3) {
      long long x = rand() % (r - l + 1) + 1;
      auto it = st.upper_bound({l, n + 1, 0});
      --it;
      multiset<pair<long long, long long>> nums;
      while (it != st.end() && it->l <= r) {
        long long len = min(it->r, r) - max(it->l, l) + 1;
        nums.insert({it->v, len});
        ++it;
      }
      for (auto i : nums) {
        x -= i.second;
        if (x <= 0) {
          cout << i.first << '\n';
          break;
        }
      }
    } else if (op == 4) {
      long long x = rand() % vmax + 1;
      long long y = rand() % vmax + 1;
      auto it = st.upper_bound({l, n + 1, 0});
      --it;
      long long ans = 0;
      while (it != st.end() && it->l <= r) {
        long long len = min(it->r, r) - max(it->l, l) + 1;
        ans += pw(it->v % y, x, y) * len % y;
        ++it;
      }
      cout << ans % y << '\n';
    }
  }
}