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;
const int maxn = 100005;
int n, m;
double x, y, a[maxn];
struct tree {
  int l, r;
  double L, R;
} t[maxn * 4];
tree merge(tree x, tree y) {
  tree z;
  z.l = x.l;
  z.r = y.r;
  z.L = x.L * y.L / (1 - (1 - y.L) * (1 - x.R));
  z.R = x.R * y.R / (1 - (1 - y.L) * (1 - x.R));
  return z;
}
void build(int l, int r, int num) {
  t[num].l = l, t[num].r = r;
  if (l == r) {
    t[num].L = a[l];
    t[num].R = 1 - a[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, num * 2);
  build(mid + 1, r, num * 2 + 1);
  t[num] = merge(t[num * 2], t[num * 2 + 1]);
}
void change(int pos, double val, int num) {
  if (t[num].l == t[num].r) {
    t[num].L = val;
    t[num].R = 1 - val;
    return;
  }
  int mid = (t[num].l + t[num].r) >> 1;
  if (pos <= mid)
    change(pos, val, num * 2);
  else
    change(pos, val, num * 2 + 1);
  t[num] = merge(t[num * 2], t[num * 2 + 1]);
}
tree ask(int L, int R, int num) {
  if (L <= t[num].l && t[num].r <= R) return t[num];
  int mid = (t[num].l + t[num].r) >> 1;
  if (R <= mid)
    return ask(L, R, num * 2);
  else if (mid < L)
    return ask(L, R, num * 2 + 1);
  else
    return merge(ask(L, R, num * 2), ask(L, R, num * 2 + 1));
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= n; ++i) {
    cin >> x >> y;
    a[i] = x / y;
  }
  build(1, n, 1);
  while (m--) {
    int opt, d;
    cin >> opt;
    if (opt == 1) {
      cin >> d >> x >> y;
      change(d, x / y, 1);
    } else {
      int l, r;
      cin >> l >> r;
      printf("%.8f\n", ask(l, r, 1).L);
    }
  }
  return 0;
}