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;
int n, m;
double b[100005];
struct node {
  double he, cheng;
} a[100005 * 4];
node merge(node a, node b) {
  node c;
  c.cheng = a.cheng * b.cheng;
  c.he = a.he + a.cheng * (b.he - 1);
  return c;
}
void build(int x, int l, int r) {
  if (l == r) {
    a[x].he = 1 + b[l];
    a[x].cheng = b[l];
    return;
  }
  int mid = (l + r) / 2;
  build(x * 2, l, mid);
  build(x * 2 + 1, mid + 1, r);
  a[x] = merge(a[x * 2], a[x * 2 + 1]);
}
void modify(int x, int l, int r, int wh, double val) {
  if (l == r) {
    a[x].cheng = val;
    a[x].he = 1 + val;
    return;
  }
  int mid = (l + r) / 2;
  if (mid >= wh)
    modify(x * 2, l, mid, wh, val);
  else
    modify(x * 2 + 1, mid + 1, r, wh, val);
  a[x] = merge(a[x * 2], a[x * 2 + 1]);
}
node query(int x, int l, int r, int tx, int ty) {
  if (l >= tx && r <= ty) return a[x];
  int mid = (l + r) / 2;
  if (mid >= tx && mid < ty)
    return merge(query(x * 2, l, mid, tx, ty),
                 query(x * 2 + 1, mid + 1, r, tx, ty));
  if (mid >= tx)
    return query(x * 2, l, mid, tx, ty);
  else
    return query(x * 2 + 1, mid + 1, r, tx, ty);
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    double x, y;
    scanf("%lf%lf", &x, &y);
    double t = x / y;
    b[i] = (1 - t) / t;
  }
  build(1, 1, n);
  while (m--) {
    int type;
    scanf("%d", &type);
    if (type == 1) {
      int wh;
      scanf("%d", &wh);
      double x, y;
      scanf("%lf%lf", &x, &y);
      double t = x / y;
      t = (1 - t) / t;
      modify(1, 1, n, wh, t);
    } else {
      int x, y;
      scanf("%d%d", &x, &y);
      printf("%.10lf\n", 1.0 / query(1, 1, n, x, y).he);
    }
  }
  return 0;
}