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>
constexpr int max_n = 1e5;
int main() {
  using namespace std;
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  cout.precision(10), cout << fixed;
  int n, q;
  cin >> n >> q;
  vector<array<double, 2>> tree(n << 1);
  for (int i = 0, a, b; i < n; ++i) {
    cin >> a >> b;
    tree[i + n] = {1.0 * a / b, 1.0 * a / b};
  }
  auto merge = [&](array<double, 2> a, array<double, 2> b) -> array<double, 2> {
    array<double, 2> res;
    res[0] = a[0] * b[0] / (1 - a[1] * (1 - b[0])),
    res[1] = b[1] + (1 - b[1]) * a[1] * b[0] / (1 - (1 - b[0]) * a[1]);
    return res;
  };
  for (int i = n - 1; i; --i) {
    tree[i] = merge(tree[i << 1], tree[i << 1 | 1]);
  }
  while (q--) {
    int type;
    cin >> type;
    if (type == 1) {
      int i, a, b;
      cin >> i >> a >> b;
      i += n - 1, tree[i][0] = tree[i][1] = 1.0 * a / b;
      for (i >>= 1; i; i >>= 1) tree[i] = merge(tree[i << 1], tree[i << 1 | 1]);
      continue;
    }
    int l, r;
    cin >> l >> r;
    array<double, 2> a = {1, 0}, b = {1, 0};
    for (l += n - 1, r += n; l < r; l >>= 1, r >>= 1) {
      if (l & 1) a = merge(a, tree[l++]);
      if (r & 1) b = merge(tree[--r], b);
    }
    cout << merge(a, b)[0] << '\n';
  }
}