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 willem = 1e9 + 7;
int n, m, k, seed, l, r, ret, ans, vmax;
long long c1, c2, a[100000 + 10], x, y;
struct seniorious {
  long long x;
  int len;
} talisman[100000 + 10];
inline int cmp(seniorious a, seniorious b) { return a.x < b.x; }
set<int> s;
set<int>::iterator p;
inline int read() {
  int x = 0;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    ;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
  return x;
}
inline int rnd() {
  ret = seed;
  seed = (seed * 7LL + 13) % willem;
  return ret;
}
inline long long quick_power(long long a, int b) {
  long long s = 1;
  for (a %= y; b; b >>= 1, a = a * a % y)
    if (b & 1) s = s * a % y;
  return s;
}
inline void write(long long x) {
  register int bit[20], p = 0, i;
  if (x == 0) {
    putchar(48);
    return;
  }
  for (; x; x /= 10) bit[++p] = x % 10;
  for (i = p; i > 0; --i) putchar(bit[i] + 48);
}
int main() {
  int i;
  n = read(), m = read(), seed = read(), vmax = read();
  for (i = 1; i <= n; ++i) a[i] = rnd() % vmax + 1;
  for (i = 0; i <= n + 1; ++i) s.insert(i);
  for (; m--;) {
    k = rnd() % 4 + 1, l = rnd() % n + 1, r = rnd() % n + 1;
    if (l > r) swap(l, r);
    x = k == 3 ? rnd() % (r - l + 1) + 1 : rnd() % vmax + 1;
    if (k == 4) y = rnd() % vmax + 1;
    if (k == 1) {
      p = --s.upper_bound(r), c2 = a[*p];
      p = s.lower_bound(r + 1);
      if (*p != r + 1) s.insert(r + 1), a[r + 1] = c2;
      p = --s.upper_bound(l), c1 = a[*p];
      if (*p != l) s.insert(l);
      a[l] = c1 + x;
      for (p = s.upper_bound(l); *p <= r; ++p) a[*p] += x;
    }
    if (k == 2) {
      p = --s.upper_bound(r), c2 = a[*p];
      p = s.lower_bound(r + 1);
      if (*p != r + 1) s.insert(r + 1), a[r + 1] = c2;
      p = --s.upper_bound(l), c1 = a[*p];
      if (*p != l) s.insert(l);
      a[l] = x;
      for (p = s.upper_bound(l); *p <= r; p = s.upper_bound(l)) s.erase(*p);
    }
    if (k == 3 || k == 4) {
      p = --s.upper_bound(l), talisman[ans = 1] = (seniorious){a[*p], l};
      for (++p; *p <= r; ++p) talisman[++ans] = (seniorious){a[*p], *p};
      for (i = 1; i <= ans; ++i)
        talisman[i].len = i == ans ? r - talisman[i].len + 1
                                   : talisman[i + 1].len - talisman[i].len;
      if (k == 3) {
        sort(talisman + 1, talisman + ans + 1, cmp);
        for (i = 1; i <= ans && x > talisman[i].len; ++i) x -= talisman[i].len;
        write(talisman[i].x), puts("");
      } else {
        long long sum = 0;
        for (i = 1; i <= ans; ++i)
          sum = (sum + quick_power(talisman[i].x, x) * talisman[i].len) % y;
        write(sum), puts("");
      }
    }
  }
}