Problem: There are n casinos lined in a row. If Memory plays at casino i, he has probability pi to win and move to the casino on the right (i + 1) or exit the row (if i = n), and a probability 1 - pi to lose and move to the casino on the left (i - 1) or also exit the row (if i = 1). 

We say that Memory dominates on the interval i... j if he completes a walk such that,

  * He starts on casino i. 
  * He never looses in casino i. 
  * He finishes his walk by winning in casino j. 



Note that Memory can still walk left of the 1-st casino and right of the casino n and that always finishes the process.

Now Memory has some requests, in one of the following forms:

  * 1 i a b: Set <image>. 
  * 2 l r: Print the probability that Memory will dominate on the interval l... r, i.e. compute the probability that Memory will first leave the segment l... r after winning at casino r, if she starts in casino l. 



It is guaranteed that at any moment of time p is a non-decreasing sequence, i.e. pi ≤ pi + 1 for all i from 1 to n - 1.

Please help Memory by answering all his requests!

Input

The first line of the input contains two integers n and q(1 ≤ n, q ≤ 100 000), — number of casinos and number of requests respectively.

The next n lines each contain integers ai and bi (1 ≤ ai < bi ≤ 109) — <image> is the probability pi of winning in casino i.

The next q lines each contain queries of one of the types specified above (1 ≤ a < b ≤ 109, 1 ≤ i ≤ n, 1 ≤ l ≤ r ≤ n).

It's guaranteed that there will be at least one query of type 2, i.e. the output will be non-empty. Additionally, it is guaranteed that p forms a non-decreasing sequence at all times.

Output

Print a real number for every request of type 2 — the probability that boy will "dominate" on that interval. Your answer will be considered correct if its absolute error does not exceed 10 - 4.

Namely: let's assume that one of your answers is a, and the corresponding answer of the jury is b. The checker program will consider your answer correct if |a - b| ≤ 10 - 4.

Example

Input

3 13
1 3
1 2
2 3
2 1 1
2 1 2
2 1 3
2 2 2
2 2 3
2 3 3
1 2 2 3
2 1 1
2 1 2
2 1 3
2 2 2
2 2 3
2 3 3


Output

0.3333333333
0.2000000000
0.1666666667
0.5000000000
0.4000000000
0.6666666667
0.3333333333
0.2500000000
0.2222222222
0.6666666667
0.5714285714
0.6666666667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10, inf = 1145141;
int rd() {
  int x = 0, w = 1;
  char ch = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + (ch ^ 48);
    ch = getchar();
  }
  return x * w;
}
struct node {
  double p, q;
  node() {}
  node(double np, double nq) { p = np, q = nq; }
  node operator+(const node &bb) const {
    return node(p * bb.p / (1 - (1 - bb.p) * (1 - q)),
                bb.q * q / (1 - (1 - q) * (1 - bb.p)));
  }
} s[N << 2];
void modif(int o, int l, int r, int lx, double x) {
  if (l == r) {
    s[o].p = x, s[o].q = 1 - x;
    return;
  }
  int mid = (l + r) >> 1;
  if (lx <= mid)
    modif(o << 1, l, mid, lx, x);
  else
    modif(o << 1 | 1, mid + 1, r, lx, x);
  s[o] = s[o << 1] + s[o << 1 | 1];
}
node quer(int o, int l, int r, int ll, int rr) {
  if (ll <= l && r <= rr) return s[o];
  int mid = (l + r) >> 1;
  if (rr <= mid) return quer(o << 1, l, mid, ll, rr);
  if (ll > mid) return quer(o << 1 | 1, mid + 1, r, ll, rr);
  return quer(o << 1, l, mid, ll, mid) +
         quer(o << 1 | 1, mid + 1, r, mid + 1, rr);
}
int n, q;
void bui(int o, int l, int r) {
  if (l == r) {
    s[o].p = rd(), s[o].p /= (double)rd(), s[o].q = 1 - s[o].p;
    return;
  }
  int mid = (l + r) >> 1;
  bui(o << 1, l, mid), bui(o << 1 | 1, mid + 1, r);
  s[o] = s[o << 1] + s[o << 1 | 1];
}
int main() {
  n = rd(), q = rd();
  bui(1, 1, n);
  while (q--) {
    int op = rd();
    if (op == 1) {
      int lc = rd();
      double x = rd();
      x /= (double)rd();
      modif(1, 1, n, lc, x);
    } else {
      int l = rd(), r = rd();
      printf("%.6lf\n", quer(1, 1, n, l, r));
    }
  }
  return 0;
}