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>
double stl[100000 * 2], str[100000 * 2];
int n;
double f(double pl, double pr, double ql) {
  return pl * ql / (1 - (1 - ql) * pr);
}
double g(double pr, double ql, double qr) {
  return qr + (1 - qr) * pr * ql / (1 - (1 - ql) * pr);
}
void pul(int i) {
  int l = i << 1, r = l | 1;
  stl[i] = f(stl[l], str[l], stl[r]), str[i] = g(str[l], stl[r], str[r]);
}
void build(double *pp) {
  int i;
  for (i = 0; i < n; i++) stl[n + i] = str[n + i] = pp[i];
  for (i = n - 1; i > 0; i--) pul(i);
}
void update(int i, double p) {
  i += n;
  stl[i] = str[i] = p;
  while (i > 1) pul(i >>= 1);
}
double query(int l, int r) {
  double pl = 1, pr = 0, ql = 1, qr = 0;
  for (l += n, r += n; l <= r; l >>= 1, r >>= 1) {
    if ((l & 1) == 1) pl = f(pl, pr, stl[l]), pr = g(pr, stl[l], str[l]), l++;
    if ((r & 1) == 0) ql = f(stl[r], str[r], ql), qr = g(str[r], ql, qr), r--;
  }
  return f(pl, pr, ql);
}
int main() {
  static double pp[100000];
  int q, i;
  scanf("%d%d", &n, &q);
  for (i = 0; i < n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    pp[i] = (double)a / b;
  }
  build(pp);
  while (q--) {
    int t;
    scanf("%d", &t);
    if (t == 1) {
      int a, b;
      scanf("%d%d%d", &i, &a, &b), i--;
      update(i, (double)a / b);
    } else {
      int l, r;
      scanf("%d%d", &l, &r), l--, r--;
      printf("%f\n", query(l, r));
    }
  }
  return 0;
}