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 = 100011;
struct Seg {
  double l, r;
  Seg operator+(Seg s) {
    Seg ret;
    ret.l = l * s.l / (1 - r * (1 - s.l));
    ret.r = s.r + r * s.l * (1 - s.r) / (1 - r * (1 - s.l));
    return ret;
  }
};
double p[N];
struct SegTree {
  Seg s[N * 4];
  void init(int l, int r, int x = 1) {
    s[x] = {p[l], p[l]};
    if (l + 1 != r) {
      init(l, (l + r) / 2, 2 * x);
      init((l + r) / 2, r, 2 * x + 1);
      s[x] = s[2 * x] + s[2 * x + 1];
    }
  }
  void change(int p, int l, int r, double c, int x = 1) {
    if (l + 1 == r)
      s[x] = {c, c};
    else {
      if (p < (l + r) / 2)
        change(p, l, (l + r) / 2, c, 2 * x);
      else
        change(p, (l + r) / 2, r, c, 2 * x + 1);
      s[x] = s[2 * x] + s[2 * x + 1];
    }
  }
  Seg query(int ql, int qr, int l, int r, int x = 1) {
    if (ql == l && qr == r) return s[x];
    if (qr <= (l + r) / 2) return query(ql, qr, l, (l + r) / 2, 2 * x);
    if (ql >= (l + r) / 2) return query(ql, qr, (l + r) / 2, r, 2 * x + 1);
    return query(ql, (l + r) / 2, l, (l + r) / 2, 2 * x) +
           query((l + r) / 2, qr, (l + r) / 2, r, 2 * x + 1);
  }
} st;
int main() {
  cout << fixed << setprecision(9);
  ios ::sync_with_stdio(false);
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    int a, b;
    cin >> a >> b;
    p[i] = (double)a / b;
  }
  st.init(1, n + 1);
  while (q--) {
    int t;
    cin >> t;
    if (t == 1) {
      int i, a, b;
      cin >> i >> a >> b;
      st.change(i, 1, n + 1, (double)a / b);
    } else {
      int l, r;
      cin >> l >> r;
      cout << st.query(l, r + 1, 1, n + 1).l << '\n';
    }
  }
  return 0;
}