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 + 3, M = 4e5 + 3;
struct T {
  double x, y;
} s[M];
double g[N];
int u, v;
T up(T a, T b) { return (T){a.x * b.x, a.y + a.x * b.y}; }
void build(int k, int l, int r) {
  if (l == r) {
    s[k].x = s[k].y = g[l];
    return;
  }
  int m = l + r >> 1;
  build(k * 2, l, m), build(k * 2 + 1, m + 1, r);
  s[k] = up(s[k * 2], s[k * 2 + 1]);
}
void upd(int k, int l, int r) {
  if (l == r) {
    s[k].x = s[k].y = g[l];
    return;
  }
  int m = l + r >> 1;
  if (u <= m)
    upd(k * 2, l, m);
  else
    upd(k * 2 + 1, m + 1, r);
  s[k] = up(s[k * 2], s[k * 2 + 1]);
}
T qry(int k, int l, int r) {
  if (u <= l && r <= v) return s[k];
  int m = l + r >> 1;
  if (u <= m && m < v) return up(qry(k * 2, l, m), qry(k * 2 + 1, m + 1, r));
  if (u <= m) return qry(k * 2, l, m);
  return qry(k * 2 + 1, m + 1, r);
}
int main() {
  int n, q, i, j, k;
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; ++i) {
    scanf("%d%d", &j, &k);
    g[i] = (k - j) * 1.0 / j;
  }
  build(1, 1, n);
  while (q--) {
    scanf("%d%d%d", &i, &j, &k);
    if (i == 1) {
      scanf("%d", &i);
      g[j] = (i - k) * 1.0 / k, u = j;
      upd(1, 1, n);
    } else {
      u = j, v = k;
      printf("%lf\n", 1 / (1 + qry(1, 1, n).y));
    }
  }
  return 0;
}