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>
const int Maxn = 100000 + 5;
double a, b;
struct node {
  int l, r;
  double L, R;
} T[Maxn << 2];
void Up(int num) {
  int l = num << 1, r = num << 1 | 1;
  T[num].L = T[l].L * T[r].L / (1 + T[l].R * (T[r].L - 1));
  T[num].R =
      T[r].R + T[l].R * T[r].L * (1 - T[r].R) / (1 - T[l].R * (1 - T[r].L));
}
node hb(node a, node b) {
  node c;
  c.l = a.l;
  c.r = b.r;
  c.L = a.L * b.L / (1 + a.R * (b.L - 1));
  c.R = b.R + a.R * b.L * (1 - b.R) / (1 - a.R * (1 - b.L));
  return c;
}
void build(int l, int r, int num) {
  T[num].l = l;
  T[num].r = r;
  if (l == r) {
    scanf("%lf%lf", &a, &b);
    T[num].L = T[num].R = a / b;
    return;
  }
  int mid = l + r >> 1;
  build(l, mid, num << 1);
  build(mid + 1, r, num << 1 | 1);
  Up(num);
}
void Update(int v, double p, int l, int r, int num) {
  if (l == r) {
    T[num].L = T[num].R = p;
    return;
  }
  int mid = l + r >> 1;
  if (v <= mid)
    Update(v, p, l, mid, num << 1);
  else
    Update(v, p, mid + 1, r, num << 1 | 1);
  Up(num);
}
node query(int l, int r, int num) {
  if (l == T[num].l && r == T[num].r) return T[num];
  int mid = T[num].l + T[num].r >> 1;
  if (r <= mid)
    return query(l, r, num << 1);
  else if (l > mid)
    return query(l, r, num << 1 | 1);
  else
    return hb(query(l, mid, num << 1), query(mid + 1, r, num << 1 | 1));
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  build(1, n, 1);
  while (q--) {
    int k;
    scanf("%d", &k);
    if (k == 1) {
      double x, y;
      int v;
      scanf("%d%lf%lf", &v, &x, &y);
      Update(v, x / y, 1, n, 1);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      printf("%.10f\n", query(l, r, 1).L);
    }
  }
  return 0;
}