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 NMAX = 100005;
int n, query;
double U[NMAX], A[4 * NMAX], B[4 * NMAX];
void creatTree(int k, int l, int r) {
  if (l == r) {
    A[k] = U[l];
    B[k] = U[l];
    return;
  }
  int mid = (l + r) / 2;
  creatTree(k * 2, l, mid);
  creatTree(k * 2 + 1, mid + 1, r);
  A[k] = A[k * 2] * A[k * 2 + 1];
  B[k] = B[k * 2] + A[k * 2] * B[k * 2 + 1];
}
void update(int k, int l, int r, int x, double u) {
  if (x < l || r < x) return;
  if (l == r) {
    A[k] = u;
    B[k] = u;
    return;
  }
  int mid = (l + r) / 2;
  update(k * 2, l, mid, x, u);
  update(k * 2 + 1, mid + 1, r, x, u);
  A[k] = A[k * 2] * A[k * 2 + 1];
  B[k] = B[k * 2] + A[k * 2] * B[k * 2 + 1];
}
double getA(int k, int l, int r, int x, int y) {
  if (y < l || r < x) return 1;
  if (x <= l && r <= y) return A[k];
  int mid = (l + r) / 2;
  return getA(k * 2, l, mid, x, y) * getA(k * 2 + 1, mid + 1, r, x, y);
}
double getB(int k, int l, int r, int x, int y) {
  if (y < l || r < x) return 0;
  if (x <= l && r <= y) {
    if (x < l) return B[k] * getA(1, 1, n, x, l - 1);
    return B[k];
  }
  int mid = (l + r) / 2;
  return getB(k * 2, l, mid, x, y) + getB(k * 2 + 1, mid + 1, r, x, y);
}
void init() {
  int a, b;
  for (int i = 1; i <= n; i++) {
    scanf("%d%d", &a, &b);
    U[i] = (double)(b) / a - 1;
  }
  creatTree(1, 1, n);
}
int main() {
  scanf("%d%d", &n, &query);
  init();
  while (query--) {
    int key;
    scanf("%d", &key);
    if (key == 2) {
      int l, r;
      scanf("%d%d", &l, &r);
      float res = getB(1, 1, n, l, r);
      if (res < 1E30)
        res = (1.0) / (1.0 + res);
      else
        res = 0;
      cout << res << "\n";
    } else {
      int a, b, x;
      scanf("%d%d%d", &x, &a, &b);
      double u = (double)(b) / a - 1;
      update(1, 1, n, x, u);
    }
  }
  return 0;
}