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 = 101000;
struct node {
  double p, sp;
} tr[maxn * 6];
int n, m;
void pushup(int st) {
  tr[st].p = (tr[st << 1].p * tr[st << 1 | 1].p);
  tr[st].sp = tr[st << 1].sp + tr[st << 1 | 1].sp * tr[st << 1].p;
}
void build(int l, int r, int st) {
  if (l == r) {
    double a, b, p;
    scanf("%lf %lf", &a, &b);
    p = a / b;
    tr[st].p = tr[st].sp = (1 - p) / p;
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, st << 1);
  build(mid + 1, r, st << 1 | 1);
  pushup(st);
}
void change(int l, int r, int st, int x) {
  if (l == r) {
    double a, b, p;
    scanf("%lf %lf", &a, &b);
    p = a / b;
    tr[st].p = tr[st].sp = (1 - p) / p;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    change(l, mid, st << 1, x);
  else
    change(mid + 1, r, st << 1 | 1, x);
  pushup(st);
}
double p, sp;
void Query(int l, int r, int st, int L, int R) {
  if (L == l && R == r) {
    sp += tr[st].sp * p;
    p *= tr[st].p;
    return;
  }
  int mid = (l + r) >> 1;
  if (R <= mid)
    Query(l, mid, st << 1, L, R);
  else if (L > mid)
    Query(mid + 1, r, st << 1 | 1, L, R);
  else {
    Query(l, mid, st << 1, L, mid);
    Query(mid + 1, r, st << 1 | 1, mid + 1, R);
  }
}
int main() {
  scanf("%d %d", &n, &m);
  build(1, n, 1);
  int op, l, r;
  while (m--) {
    scanf("%d", &op);
    if (op == 1) {
      scanf("%d", &l);
      change(1, n, 1, l);
    } else {
      p = 1;
      sp = 0;
      scanf("%d %d", &l, &r);
      Query(1, n, 1, l, r);
      double ans = 0;
      if (sp < 1e15) ans = (1.0 / (sp + 1));
      printf("%.10f\n", ans);
    }
  }
  return 0;
}