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;
pair<double, double> seg[4 * 111111];
double p[111111];
int n, q;
pair<double, double> merge(pair<double, double> x, pair<double, double> y) {
  return make_pair(x.first * y.first / (1. + x.second * (y.first - 1.)),
                   y.second + x.second * y.first * (1. - y.second) /
                                  (1. - x.second * (1. - y.first)));
}
pair<double, double> query(int id, int l, int r, int ql, int qr) {
  if (l == ql && r == qr) return seg[id];
  int m = (l + r) / 2;
  if (qr <= m) return query(2 * id, l, m, ql, qr);
  if (ql >= m) return query(2 * id + 1, m, r, ql, qr);
  return merge(query(2 * id, l, m, ql, m), query(2 * id + 1, m, r, m, qr));
}
void update(int id, int l, int r, int x, double P) {
  if (l + 1 == r) {
    p[l] = P;
    seg[id] = make_pair(P, P);
    return;
  }
  int m = (l + r) / 2;
  if (x < m)
    update(2 * id, l, m, x, P);
  else
    update(2 * id + 1, m, r, x, P);
  seg[id] = merge(seg[2 * id], seg[2 * id + 1]);
}
void build(int id, int l, int r) {
  if (l + 1 == r) {
    seg[id] = make_pair(p[l], p[l]);
    return;
  }
  int m = (l + r) / 2;
  build(2 * id, l, m);
  build(2 * id + 1, m, r);
  seg[id] = merge(seg[2 * id], seg[2 * id + 1]);
}
int main() {
  cin >> n >> q;
  for (int i = 0; i < n; i++) {
    double a, b;
    cin >> a >> b;
    p[i] = a / b;
  }
  build(1, 0, n);
  while (q--) {
    double a, b, c, d;
    cin >> a >> b >> c;
    b--;
    if (a == 1) {
      cin >> d;
      update(1, 0, n, b, c / d);
    } else {
      cout << fixed << setprecision(10) << query(1, 0, n, b, c).first << endl;
    }
  }
  return 0;
}