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 = 1e5 + 10, M = 0, Z = 1e9 + 7, ms63 = 0x3f3f3f3f;
int n, q;
pair<double, double> a[1 << 18];
pair<double, double> merge(pair<double, double> x, pair<double, double> y) {
  double l1 = x.first;
  double r1 = x.second;
  double l2 = y.first;
  double r2 = y.second;
  double l = (l1 * l2) / (1 - (1 - l2) * r1);
  double r = r2 + ((1 - r2) * r1 * l2) / (1 - (1 - l2) * r1);
  return {l, r};
}
void build(int o, int l, int r) {
  if (l == r) {
    double x, y;
    scanf("%lf%lf", &x, &y);
    a[o] = {x / y, x / y};
    return;
  }
  int mid = (l + r) >> 1;
  build(o << 1, l, mid);
  build(o << 1 | 1, mid + 1, r);
  a[o] = merge(a[o << 1], a[o << 1 | 1]);
}
pair<double, double> V;
int P;
void update(int o, int l, int r) {
  if (l == r) {
    a[o] = V;
    return;
  }
  int mid = (l + r) >> 1;
  if (P <= mid)
    update(o << 1, l, mid);
  else
    update(o << 1 | 1, mid + 1, r);
  a[o] = merge(a[o << 1], a[o << 1 | 1]);
}
int L, R;
pair<double, double> query(int o, int l, int r) {
  if (l >= L && r <= R) return a[o];
  int mid = (l + r) >> 1;
  if (R <= mid)
    return query(o << 1, l, mid);
  else if (L > mid)
    return query(o << 1 | 1, mid + 1, r);
  else
    return merge(query(o << 1, l, mid), query(o << 1 | 1, mid + 1, r));
}
int main() {
  while (~scanf("%d%d", &n, &q)) {
    build(1, 1, n);
    while (q--) {
      int op;
      scanf("%d", &op);
      if (op == 1) {
        double x, y;
        scanf("%d%lf%lf", &P, &x, &y);
        V = {x / y, x / y};
        update(1, 1, n);
      } else {
        scanf("%d%d", &L, &R);
        printf("%.12f\n", query(1, 1, n).first);
      }
    }
  }
  return 0;
}