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 seg {
  double a, b;
} t[100005 * 4], now;
int n, q;
double p[100005];
void build(int v, int l, int r) {
  if (l == r) {
    t[v].a = t[v].b = (1 - p[l]) / p[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(v << 1, l, mid);
  build(v << 1 | 1, mid + 1, r);
  t[v].a = t[v << 1].a * t[v << 1 | 1].a;
  if (t[v].a > 1e310)
    while (1)
      ;
  t[v].b = t[v << 1].b + t[v << 1 | 1].b * t[v << 1].a;
}
void change(int v, int l, int r, int x) {
  if (l == r) {
    t[v].a = t[v].b = (1 - p[l]) / p[l];
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    change(v << 1, l, mid, x);
  else
    change(v << 1 | 1, mid + 1, r, x);
  t[v].a = t[v << 1].a * t[v << 1 | 1].a;
  t[v].b = t[v << 1].b + t[v << 1 | 1].b * t[v << 1].a;
}
void query(int v, int l, int r, int x, int y) {
  if (l == x && r == y) {
    now.b = now.b + now.a * t[v].b;
    now.a = now.a * t[v].a;
    return;
  }
  int mid = (l + r) >> 1;
  if (y <= mid)
    query(v << 1, l, mid, x, y);
  else if (x > mid)
    query(v << 1 | 1, mid + 1, r, x, y);
  else
    query(v << 1, l, mid, x, mid), query(v << 1 | 1, mid + 1, r, mid + 1, y);
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    p[i] = 1.0 * x / y;
  }
  build(1, 1, n);
  while (q--) {
    int Type, x, y, z;
    scanf("%d", &Type);
    if (Type == 1) {
      scanf("%d%d%d", &x, &y, &z);
      p[x] = 1.0 * y / z;
      change(1, 1, n, x);
    } else {
      scanf("%d%d", &x, &y);
      double ans;
      now.a = 1;
      now.b = 0;
      query(1, 1, n, x, y);
      if (now.b <= 1e15)
        ans = 1 / (1 + now.b);
      else
        ans = 0;
      printf("%.10lf\n", ans);
    }
  }
  return 0;
}