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 = 2e6 + 1, INF = 1e9 + 1;
int n, q, a, b, p, t;
pair<long double, long double> st[N], lf, rg;
pair<long double, long double> merge(pair<long double, long double> a,
                                     pair<long double, long double> b) {
  long double l1 = a.first, r1 = a.second, l2 = b.first, r2 = b.second;
  if (a.first < 0 and a.second < 0) return b;
  if (b.first < 0 and b.second < 0) return a;
  return pair<long double, long double>(
      l1 * l2 / (1 - r1 * (1 - l2)),
      r2 + r1 * l2 * (1 - r2) / (1 - (r1 * (1 - l2))));
}
pair<long double, long double> query(int l, int r) {
  lf = rg = pair<long double, long double>(-1, -1);
  l += n - 1, r += n;
  while (l < r) {
    if (l & 1) lf = merge(lf, st[l++]);
    if (r & 1) rg = merge(st[--r], rg);
    l /= 2, r /= 2;
  }
  return merge(lf, rg);
}
void update(int k, long double v) {
  k += n - 1;
  st[k] = pair<long double, long double>(v, v);
  while (k) k /= 2, st[k] = merge(st[2 * k], st[2 * k + 1]);
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = n; i < 2 * n; ++i) {
    scanf("%d%d", &a, &b);
    st[i] = pair<long double, long double>(1.0 * a / b, 1.0 * a / b);
  }
  for (int i = n - 1; i >= 0; --i) st[i] = merge(st[2 * i], st[2 * i + 1]);
  for (int i = 0; i < q; ++i) {
    scanf("%d", &t);
    if (t == 1) {
      scanf("%d%d%d", &p, &a, &b);
      update(p, 1.0L * a / b);
    } else {
      scanf("%d%d", &a, &b);
      printf("%lf\n", (double)query(a, b).first);
    }
  }
  return 0;
}