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 {
  int l, r;
  double v, w;
} s[100005 << 2];
void build(int k, int l, int r) {
  s[k].l = l;
  s[k].r = r;
  if (l == r) return;
  int mid = (l + r) >> 1;
  build(k << 1, l, mid);
  build(k << 1 | 1, mid + 1, r);
}
void modify(int k, int x, double v) {
  if (s[k].l == s[k].r) {
    s[k].v = s[k].w = (1 - v) / v;
    return;
  }
  int mid = (s[k].l + s[k].r) >> 1;
  if (x <= mid)
    modify(k << 1, x, v);
  else
    modify(k << 1 | 1, x, v);
  s[k].v = s[k << 1].v * s[k << 1 | 1].v;
  s[k].w = s[k << 1].w + s[k << 1].v * s[k << 1 | 1].w;
}
double query(int k, int l, int r) {
  if (l <= s[k].l && s[k].r <= r) return s[k].v;
  int mid = (s[k].l + s[k].r) >> 1;
  if (r <= mid)
    return query(k << 1, l, r);
  else if (l > mid)
    return query(k << 1 | 1, l, r);
  else
    return query(k << 1, l, mid) * query(k << 1 | 1, mid + 1, r);
}
double queryw(int k, int l, int r) {
  if (l <= s[k].l && s[k].r <= r) return s[k].w;
  int mid = (s[k].l + s[k].r) >> 1;
  if (r <= mid)
    return queryw(k << 1, l, r);
  else if (l > mid)
    return queryw(k << 1 | 1, l, r);
  else
    return queryw(k << 1, l, mid) +
           query(k << 1, l, mid) * queryw(k << 1 | 1, mid + 1, r);
}
int n, q;
int main() {
  scanf("%d%d", &n, &q);
  build(1, 1, n);
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    modify(1, i, 1.0 * a / b);
  }
  for (int i = 1; i <= q; i++) {
    int opt;
    scanf("%d", &opt);
    if (opt == 1) {
      int x, a, b;
      scanf("%d%d%d", &x, &a, &b);
      modify(1, x, 1.0 * a / b);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      double mul = queryw(1, l, r);
      printf("%.16lf\n", 1.0 / (1.0 + mul));
    }
  }
  return 0;
}