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;
const int BUF_SIZE = 1 << 12;
char buf[BUF_SIZE], *buf_s = buf, *buf_t = buf + 1;
template <typename _m_>
void mian(_m_ &_n_) {
  int _x_ = 0, _nega_ = 0;
  while (*buf_s != '-' && !isdigit(*buf_s)) {
    buf_s++;
    if (buf_s == buf_t) {
      buf_s = buf;
      buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
    }
  };
  if (*buf_s == '-') {
    _nega_ = 1;
    {
      buf_s++;
      if (buf_s == buf_t) {
        buf_s = buf;
        buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
      }
    };
  }
  while (isdigit(*buf_s)) {
    _x_ = _x_ * 10 + *buf_s - '0';
    {
      buf_s++;
      if (buf_s == buf_t) {
        buf_s = buf;
        buf_t = buf + fread(buf, 1, BUF_SIZE, stdin);
      }
    };
  }
  if (_nega_) _x_ = -_x_;
  (_n_) = (_x_);
}
inline long long quick_pow(long long a, long long b, long long mod) {
  long long res = 1;
  a %= mod;
  for (; b; b >>= 1, a = a * a % mod) {
    if (b & 1) {
      res = res * a % mod;
    }
  }
  return res % mod;
}
const long long kato = 1e5 + 10;
long long n, m, seed, vmax, a[kato];
struct Chtholly_Tree {
 public:
  struct tag {
    long long v, del;
    tag(long long v = 0, long long del = 0) : v(v), del(del) {}
    bool operator<(const tag &a) const { return a.v > v; }
  };
  struct node {
    long long l, r;
    mutable long long val;
    node(long long l = 0, long long r = -1, long long val = 0)
        : l(l), r(r), val(val) {}
    bool operator<(const node &a) const { return a.l > l; }
  };
  set<node> ODT;
  inline set<node>::iterator split(long long pos) {
    auto it = ODT.lower_bound(node(pos));
    if (it != ODT.end() && it->l == pos) return it;
    it--;
    long long L = it->l, R = it->r;
    long long V = it->val;
    ODT.erase(it);
    ODT.insert(node(L, pos - 1, V));
    return ODT.insert(node(pos, R, V)).first;
  }
  inline void add(long long l, long long r, long long v) {
    auto itl = split(l), itr = split(r + 1);
    for (; itl != itr; itl++) {
      itl->val += v;
    }
  }
  inline void assign_val(long long l, long long r, long long v) {
    auto itl = split(l), itr = split(r + 1);
    ODT.erase(itl, itr);
    ODT.insert(node(l, r, v));
  }
  inline long long rank(long long l, long long r, long long k) {
    vector<tag> up;
    auto itl = split(l), itr = split(r + 1);
    up.clear();
    for (; itl != itr; itl++) {
      up.push_back(tag(itl->val, itl->r - itl->l + 1));
    }
    sort(up.begin(), up.end());
    for (auto it = up.begin(); it != up.end(); it++) {
      k = k - it->del;
      if (k <= 0) return it->v;
    }
  }
  inline long long get_sum(long long l, long long r, long long ex,
                           long long mod) {
    auto itl = split(l), itr = split(r + 1);
    long long res = 0;
    for (; itl != itr; itl++) {
      res = (res + 1LL * (itl->r - itl->l + 1) *
                       quick_pow(itl->val, 1LL * ex, 1LL * mod) % mod) %
            mod;
    }
    return res;
  }
  inline long long rand_() {
    long long res = seed;
    seed = (seed * 7 + 13) % 1000000007;
    return res;
  }
  inline void build(long long l, long long r, long long val) {
    ODT.insert(node(l, r, val));
  }
} yuni;
inline long long Ame_() {
  mian(n), mian(m), mian(seed), mian(vmax);
  for (long long i = 1; i <= n; i++) {
    a[i] = (yuni.rand_() % vmax) + 1;
    yuni.build(i, i, a[i]);
  }
  yuni.build(n + 1, n + 1, 0);
  for (; m-- > 0;) {
    long long opt = (yuni.rand_() % 4) + 1;
    long long l = (yuni.rand_() % n) + 1;
    long long r = (yuni.rand_() % n) + 1;
    if (l > r) swap(l, r);
    long long x, y;
    if (opt == 3)
      x = (yuni.rand_() % (r - l + 1)) + 1;
    else
      x = (yuni.rand_() % vmax) + 1;
    if (opt == 4) y = (yuni.rand_() % vmax) + 1;
    if (opt == 1) yuni.add(l, r, x);
    if (opt == 2) yuni.assign_val(l, r, x);
    if (opt == 3) printf("%lld\n", yuni.rank(l, r, x));
    if (opt == 4) printf("%lld\n", yuni.get_sum(l, r, x, y));
  }
  return ~~(0 ^ 0 ^ 0);
}
long long Ame__ = Ame_();
signed main() { ; }