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 gi() {
  char cc = getchar();
  int cn = 0, flus = 1;
  while (cc < '0' || cc > '9') {
    if (cc == '-') flus = -flus;
    cc = getchar();
  }
  while (cc >= '0' && cc <= '9') cn = cn * 10 + cc - '0', cc = getchar();
  return cn * flus;
}
const int N = 2e5 + 5;
const double eps = 1e-9;
int n, q;
double p[N];
struct Tr {
  double f, g;
} tr[N << 1];
Tr pushup(Tr x, Tr y) {
  Tr u;
  u.f = x.f * y.f / (x.g + y.f - x.g * y.f + eps);
  u.g = x.g * y.g / (x.g + y.f - x.g * y.f + eps);
  return u;
}
Tr query(int x, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[x];
  int mid = (l + r) >> 1;
  if (mid >= qr) return query((x << 1), l, mid, ql, qr);
  if (mid < ql) return query((x << 1 | 1), mid + 1, r, ql, qr);
  return pushup(query((x << 1), l, mid, ql, mid),
                query((x << 1 | 1), mid + 1, r, mid + 1, qr));
}
void update(int x, int l, int r, int wh) {
  if (l == r) {
    tr[x].f = p[l], tr[x].g = 1 - p[l];
    return;
  }
  int mid = (l + r) >> 1;
  if (wh <= mid)
    update((x << 1), l, mid, wh);
  else
    update((x << 1 | 1), mid + 1, r, wh);
  tr[x] = pushup(tr[(x << 1)], tr[(x << 1 | 1)]);
}
void build(int x, int l, int r) {
  if (l == r) {
    tr[x].f = p[l], tr[x].g = 1 - p[l];
    return;
  }
  int mid = (l + r) >> 1;
  build((x << 1), l, mid), build((x << 1 | 1), mid + 1, r);
  tr[x] = pushup(tr[(x << 1)], tr[(x << 1 | 1)]);
}
signed main() {
  n = gi(), q = gi();
  int x, y;
  for (register int i = (1); i <= (n); ++i)
    x = gi(), y = gi(), p[i] = (1.0 * x) / (1.0 * y);
  build(1, 1, n);
  for (register int i = (1); i <= (q); ++i) {
    int opt = gi(), l = gi(), r = gi();
    if (opt == 1) x = gi(), p[l] = (1.0 * r) / (1.0 * x), update(1, 1, n, l);
    if (opt == 2) printf("%.7lf\n", query(1, 1, n, l, r).f);
  }
  return 0;
}