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;
struct Node {
  long double l, r;
};
Node merge(Node a, Node b) {
  if (a.l < -1 && a.r < -1) return b;
  if (b.l < -1 && b.r < -1) return a;
  Node c;
  c.l = a.l * b.l / (1 - (1 - b.l) * (1 - a.r));
  c.r = b.r * a.r / (1 - (1 - a.r) * (1 - b.l));
  return c;
}
Node st[3 * 101010];
int n, q;
void upd(int p, long double v, int b = 1, int l = 1, int r = n) {
  if (p < l || p > r) return;
  if (l == r) {
    st[b].l = v;
    st[b].r = 1 - v;
    return;
  }
  int fe = b << 1, fd = fe | 1, mid = (l + r) >> 1;
  upd(p, v, fe, l, mid);
  upd(p, v, fd, mid + 1, r);
  st[b] = merge(st[fe], st[fd]);
}
Node query(int first, int second, int b = 1, int l = 1, int r = n) {
  if (second < l || r < first) {
    Node ret;
    ret.l = -2, ret.r = -2;
    return ret;
  }
  if (first <= l && r <= second) return st[b];
  int fe = b << 1, fd = fe | 1, mid = (l + r) >> 1;
  return merge(query(first, second, fe, l, mid),
               query(first, second, fd, mid + 1, r));
}
int main() {
  scanf("%d%d", &n, &q);
  for (int(i) = (1); (i) < (n + 1); (i)++) {
    int a, b;
    scanf("%d%d", &a, &b);
    upd(i, (long double)a / (long double)b);
  }
  for (int(i) = (0); (i) < (q); (i)++) {
    int tp;
    scanf("%d", &tp);
    if (tp == 1) {
      int p, a, b;
      scanf("%d%d%d", &p, &a, &b);
      upd(p, (long double)a / (long double)b);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      Node aux = query(l, r);
      printf("%.10f\n", (double)aux.l);
    }
  }
}