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;
int read() {
  bool f = 0;
  int x = 0;
  char c = getchar();
  while (c < '0' || '9' < c) {
    if (c == '-') f = 1;
    c = getchar();
  }
  while ('0' <= c && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  return !f ? x : -x;
}
struct node {
  double l, r;
  friend node operator+(node a, node b) {
    node c;
    c.l = a.l * b.l / (1 - a.r * (1 - b.l)),
    c.r = b.r + (1 - b.r) * b.l * a.r / (1 - a.r * (1 - b.l));
    return c;
  }
} tree[5 * 100000 + 5];
double P[100000 + 5], l[5 * 100000 + 5], r[5 * 100000 + 5];
void PushUp(int i) {
  tree[i] = tree[(i << 1)] + tree[(i << 1 | 1)];
  return;
}
void Build(int i, int L, int R) {
  if (L == R) {
    tree[i] = (node){P[L], P[L]};
    return;
  }
  int Mid = (L + R) >> 1;
  Build((i << 1), L, Mid), Build((i << 1 | 1), Mid + 1, R);
  PushUp(i);
  return;
}
void Insert(int i, int L, int R, int p, double x) {
  if (L == R) {
    tree[i] = (node){x, x};
    return;
  }
  int Mid = (L + R) >> 1;
  if (p <= Mid)
    Insert((i << 1), L, Mid, p, x);
  else
    Insert((i << 1 | 1), Mid + 1, R, p, x);
  PushUp(i);
  return;
}
node Query(int i, int L, int R, int qL, int qR) {
  if (qL <= L && R <= qR) return tree[i];
  int Mid = (L + R) >> 1;
  if (qR <= Mid)
    return Query((i << 1), L, Mid, qL, qR);
  else if (Mid + 1 <= qL)
    return Query((i << 1 | 1), Mid + 1, R, qL, qR);
  return Query((i << 1), L, Mid, qL, Mid) +
         Query((i << 1 | 1), Mid + 1, R, Mid + 1, qR);
}
int main() {
  int n = read(), q = read();
  for (int i = 1; i <= n; i++) {
    int a = read(), b = read();
    P[i] = 1.0 * a / b;
  }
  Build(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int opt = read();
    if (opt == 1) {
      int p = read(), a = read(), b = read();
      Insert(1, 1, n, p, 1.0 * a / b);
    } else {
      int l = read(), r = read();
      printf("%.10lf\n", Query(1, 1, n, l, r).l);
    }
  }
  return 0;
}