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 N = 1e5 + 100;
double ff[N << 2], gg[N << 2];
double aa[N], bb[N];
double fun(double f1, double g1, double f2, double g2) {
  return f1 * f2 / (1 - (1 - f2) * g1);
}
double gun(double f1, double g1, double f2, double g2) {
  return g2 + (1 - g2) * g1 * f2 / (1 - (1 - f2) * g1);
}
void up(int o) {
  ff[o] = fun(ff[o << 1], gg[o << 1], ff[o << 1 | 1], gg[o << 1 | 1]);
  gg[o] = gun(ff[o << 1], gg[o << 1], ff[o << 1 | 1], gg[o << 1 | 1]);
}
void build(int l, int r, int o) {
  if (l == r) {
    ff[o] = gg[o] = aa[l] / bb[l];
    return;
  }
  build(l, (l + r) / 2, o << 1);
  build((l + r) / 2 + 1, r, o << 1 | 1);
  up(o);
}
int L, R;
double V;
void update(int l, int r, int o, int x) {
  if (l == r) {
    ff[o] = gg[o] = V;
    return;
  }
  if (x <= (l + r) / 2)
    update(l, (l + r) / 2, o << 1, x);
  else
    update((l + r) / 2 + 1, r, o << 1 | 1, x);
  up(o);
}
double f1, g1;
int fg;
void query(int l, int r, int o) {
  if (L <= l && r <= R) {
    if (!fg) {
      fg = 1;
      f1 = ff[o], g1 = gg[o];
      return;
    }
    double f2 = fun(f1, g1, ff[o], gg[o]);
    double g2 = gun(f1, g1, ff[o], gg[o]);
    f1 = f2, g1 = g2;
    return;
  }
  if (L <= (l + r) / 2) query(l, (l + r) / 2, o << 1);
  if (R > (l + r) / 2) query((l + r) / 2 + 1, r, o << 1 | 1);
}
int main() {
  int n, q;
  while (scanf("%d%d", &n, &q) != EOF) {
    for (int i = 0; i < n; i++) {
      scanf("%lf%lf", &aa[i], &bb[i]);
    }
    build(0, n - 1, 1);
    for (int i = 0; i < q; i++) {
      int op, id, l, r;
      scanf("%d", &op);
      if (op == 1) {
        scanf("%d%d%d", &id, &l, &r);
        V = (double)l / r;
        update(0, n - 1, 1, id - 1);
      } else {
        scanf("%d%d", &L, &R);
        L--, R--;
        fg = 0;
        query(0, n - 1, 1);
        printf("%.10lf\n", f1);
      }
    }
  }
  return 0;
}