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;
double t[100100], t1, t2;
int n, q, type, st, en, w;
struct line_tree {
  double sum_up, single;
} tr[2332333], nil;
line_tree together(line_tree tr1, line_tree tr2) {
  return (line_tree){tr1.sum_up + tr1.single * tr2.sum_up,
                     tr1.single * tr2.single};
}
line_tree build(int x, int l, int r) {
  if (l == r) return tr[x] = (line_tree){t[l], t[l]};
  return tr[x] = together(build(x << 1, l, ((l + r) >> 1)),
                          build(x << 1 | 1, ((l + r) >> 1) + 1, r));
}
line_tree change(int x, int l, int r, int p) {
  if (l > p || r < p) return tr[x];
  if (l == r) return tr[x] = (line_tree){t[l], t[l]};
  return tr[x] = together(change(x << 1, l, ((l + r) >> 1), p),
                          change(x << 1 | 1, ((l + r) >> 1) + 1, r, p));
}
line_tree que(int x, int l, int r, int st, int en) {
  if (l == st && r == en) return tr[x];
  if (en <= ((l + r) >> 1)) return que(x << 1, l, ((l + r) >> 1), st, en);
  if (st > ((l + r) >> 1))
    return que(x << 1 | 1, ((l + r) >> 1) + 1, r, st, en);
  return together(
      que(x << 1, l, ((l + r) >> 1), st, ((l + r) >> 1)),
      que(x << 1 | 1, ((l + r) >> 1) + 1, r, ((l + r) >> 1) + 1, en));
}
int main() {
  nil.single = 1;
  nil.sum_up = 0;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    cin >> t1 >> t2;
    t[i] = (1.0 - (t1 / t2)) / (t1 / t2);
  }
  build(1, 1, n);
  while (q--) {
    cin >> type;
    if (type == 1) {
      cin >> w >> t1 >> t2;
      t[w] = (1.0 - (t1 / t2)) / (t1 / t2);
      change(1, 1, n, w);
    } else {
      cin >> st >> en;
      t1 = que(1, 1, n, st, en).sum_up;
      printf("%.10lf\n", t1 > 1e15 ? 0 : 1.0 / (t1 + 1));
    }
  }
}