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 + 100;
const double DOUBLE_MIN = 1e-15;
struct Data {
  Data() : f(0), g(0) {}
  Data(double ff, double gg) : f(ff), g(gg) {}
  double f;
  double g;
};
Data tr[4 * N];
double p[N];
Data merge(const Data &d1, const Data &d2) {
  Data res;
  const double &l1 = d1.f;
  const double &r1 = d1.g;
  const double &l2 = d2.f;
  const double &r2 = d2.g;
  double tmp;
  tmp = (1 - r1 * (1 - l2));
  if (tmp < DOUBLE_MIN) {
    res.f = res.g = 0;
  } else {
    res.f = l1 * l2 / (1 - r1 * (1 - l2));
    res.g = r2 + (1 - r2) * r1 * l2 / (1 - r1 * (1 - l2));
  }
  return res;
}
void build(int idx, int left, int right) {
  if (left == right) {
    tr[idx].f = p[left];
    tr[idx].g = p[left];
    return;
  }
  int mid = (left + right) / 2;
  build(idx * 2, left, mid);
  build(idx * 2 + 1, mid + 1, right);
  tr[idx] = merge(tr[idx * 2], tr[idx * 2 + 1]);
}
void update(int idx, int i, int left, int right) {
  if (i < left || i > right) {
    return;
  }
  if (left == right) {
    tr[idx].f = p[left];
    tr[idx].g = p[left];
    return;
  }
  int mid = (left + right) / 2;
  update(idx * 2, i, left, mid);
  update(idx * 2 + 1, i, mid + 1, right);
  tr[idx] = merge(tr[idx * 2], tr[idx * 2 + 1]);
}
Data query(int idx, int start, int end, int left, int right) {
  Data res;
  if (left == start && right == end) {
    res = tr[idx];
    return res;
  }
  int mid = (left + right) / 2;
  Data res1, res2;
  if (start >= left && end <= mid) {
    res = query(idx * 2, start, end, left, mid);
  } else if (start >= mid + 1 && end <= right) {
    res = query(idx * 2 + 1, start, end, mid + 1, right);
  } else {
    res1 = query(idx * 2, start, mid, left, mid);
    res2 = query(idx * 2 + 1, mid + 1, end, mid + 1, right);
    res = merge(res1, res2);
  }
  return res;
}
vector<double> ans;
int main() {
  int n, qNum, i, a, b, l, r, k;
  int type;
  scanf("%d%d", &n, &qNum);
  for (i = 1; i <= n; i++) {
    scanf("%d%d", &a, &b);
    p[i] = (double)a / b;
  }
  build(1, 1, n);
  for (i = 1; i <= qNum; i++) {
    scanf("%d", &type);
    if (type == 1) {
      scanf("%d%d%d", &k, &a, &b);
      p[k] = (double)a / b;
      update(1, k, 1, n);
    } else {
      scanf("%d%d", &l, &r);
      Data res = query(1, l, r, 1, n);
      ans.push_back(res.f);
    }
  }
  for (i = 0; i < ans.size(); i++) {
    printf("%.9lf\n", ans[i]);
  }
  return 0;
}