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;
int n, q;
double p[100005];
pair<double, double> merge(pair<double, double> p, pair<double, double> q) {
  if (p.first == -1.0) return q;
  if (q.first == -1.0) return p;
  double a = p.first, b = p.second, c = q.first, d = q.second;
  return pair<double, double>(a * c / (1 - b + b * c),
                              d + (1 - d) * b * c / (1 - b + b * c));
}
struct segtree {
  pair<double, double> res[4 * 100005];
  void pushup(int k) { res[k] = merge(res[k * 2], res[k * 2 + 1]); }
  void build(int k, int l, int r) {
    if (l == r) {
      res[k] = pair<double, double>(p[l], p[l]);
      return;
    }
    int mid = (l + r) / 2;
    build(k * 2, l, mid);
    build(k * 2 + 1, mid + 1, r);
    pushup(k);
  }
  void update(int k, int l, int r, int p, double v) {
    if (l == r) {
      res[k] = pair<double, double>(v, v);
      return;
    }
    int mid = (l + r) / 2;
    if (p <= mid)
      update(k * 2, l, mid, p, v);
    else
      update(k * 2 + 1, mid + 1, r, p, v);
    pushup(k);
  }
  pair<double, double> query(int k, int l, int r, int x, int y) {
    if (l > y || x > r) return pair<double, double>(-1.0, -1.0);
    if (l >= x && r <= y) return res[k];
    int mid = (l + r) / 2;
    return merge(query(k * 2, l, mid, x, y),
                 query(k * 2 + 1, mid + 1, r, x, y));
  }
} seg;
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    p[i] = (double)a / b;
  }
  seg.build(1, 1, n);
  for (int i = 0; i < q; i++) {
    int type, l, r, a, b, x;
    scanf("%d", &type);
    if (type == 1) {
      scanf("%d%d%d", &x, &a, &b);
      double pp = (double)a / b;
      seg.update(1, 1, n, x, pp);
    } else {
      scanf("%d%d", &l, &r);
      pair<double, double> ret = seg.query(1, 1, n, l, r);
      printf("%.10f\n", ret.first);
    }
  }
  return 0;
}