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>
int n, Q, x, y;
double k;
struct tree {
  double l, r;
} f[400000];
inline tree operator+(const tree A, const tree B) {
  return (tree){A.l * B.l / (1 - (1 - B.l) * A.r),
                B.r + (1 - B.r) * A.r * B.l / (1 - (1 - B.l) * A.r)};
}
inline int read() {
  char c = getchar();
  int k = 0;
  for (; c < 48 || c > 57; c = getchar())
    ;
  for (; c > 47 && c < 58; c = getchar()) k = (k << 3) + (k << 1) + c - 48;
  return k;
}
void build(int p, int l, int r) {
  if (l == r) {
    double k = (double)read() / read();
    f[p] = (tree){k, k};
    return;
  }
  int m = l + r >> 1;
  build(p << 1, l, m);
  build(p << 1 | 1, m + 1, r);
  f[p] = f[p << 1] + f[p << 1 | 1];
}
void change(int p, int l, int r) {
  if (l == r) {
    f[p] = (tree){k, k};
    return;
  }
  int m = l + r >> 1;
  if (x <= m)
    change(p << 1, l, m);
  else
    change(p << 1 | 1, m + 1, r);
  f[p] = f[p << 1] + f[p << 1 | 1];
}
tree ask(int p, int l, int r) {
  if (x <= l && r <= y) return f[p];
  int m = l + r >> 1;
  if (y <= m) return ask(p << 1, l, m);
  if (x > m) return ask(p << 1 | 1, m + 1, r);
  return ask(p << 1, l, m) + ask(p << 1 | 1, m + 1, r);
}
int main() {
  n = read();
  Q = read();
  build(1, 1, n);
  for (; Q--;) {
    int w = read();
    if (w == 1) {
      x = read();
      k = (double)read() / read();
      change(1, 1, n);
    } else {
      x = read();
      y = read();
      printf("%.10lf\n", ask(1, 1, n).l);
    }
  }
}