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;
double st[400005][2];
double p[100005];
int n, q;
void merge(double *r, double *a, double *b) {
  if (a[0] < -0.5) {
    r[0] = b[0];
    r[1] = b[1];
  } else {
    double t[2], t0, t1;
    t0 = b[0] / (1 - (1 - b[0]) * a[1]);
    t[0] = a[0] * t0;
    t1 = a[1] * t0;
    t[1] = b[1] + (1 - b[1]) * t1;
    r[0] = t[0];
    r[1] = t[1];
  }
}
void st_init(int k, int s, int e) {
  if (s + 1 == e) {
    st[k][0] = st[k][1] = p[s];
  } else {
    int m = (s + e) / 2;
    st_init(2 * k, s, m);
    st_init(2 * k + 1, m, e);
    merge(st[k], st[2 * k], st[2 * k + 1]);
  }
}
void st_upd(int k, int s, int e, int p, double v) {
  if (s + 1 == e) {
    st[k][0] = st[k][1] = v;
  } else {
    int m = (s + e) / 2;
    if (p < m)
      st_upd(2 * k, s, m, p, v);
    else
      st_upd(2 * k + 1, m, e, p, v);
    merge(st[k], st[2 * k], st[2 * k + 1]);
  }
}
void st_query(int k, int s, int e, int a, int b, double *r) {
  if (e <= a || s >= b) return;
  if (s >= a && e <= b)
    merge(r, r, st[k]);
  else {
    int m = (s + e) / 2;
    st_query(2 * k, s, m, a, b, r);
    st_query(2 * k + 1, m, e, a, b, r);
  }
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 0, to = n; i < to; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    p[i] = 1. * a / b;
  }
  st_init(1, 0, n);
  while (q--) {
    int t;
    scanf("%d", &t);
    if (t == 1) {
      int i, a, b;
      scanf("%d%d%d", &i, &a, &b);
      st_upd(1, 0, n, i - 1, 1. * a / b);
    } else {
      int a, b;
      scanf("%d%d", &a, &b);
      double r[2];
      r[0] = r[1] = -1.;
      st_query(1, 0, n, a - 1, b, r);
      printf("%.10lf\n", r[0]);
    }
  }
  return 0;
}