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 = 100005;
int n, q;
double buffer, tree[N << 1], suff[N << 1];
void pull(int a, int b, int out) {
  double p1 = tree[a];
  double s1 = suff[a];
  double p2 = tree[b];
  double s2 = suff[b];
  if (p1 < 0) {
    tree[out] = p2;
    suff[out] = s2;
    return;
  }
  if (p2 < 0) {
    tree[out] = p1;
    suff[out] = s1;
    return;
  }
  double f1 = p1 * p2 / (1 - s1 * (1 - p2));
  double g2 = s2 + (1 - s2) * s1 * p2 / (1 - s1 * (1 - p2));
  tree[out] = f1;
  suff[out] = g2;
}
void update(int i, double x) {
  tree[i + n] = x;
  suff[i + n] = x;
  for (i += n; i > 1; i >>= 1) pull(min(i, i ^ 1), max(i, i ^ 1), i >> 1);
}
double query(int a, int b) {
  int left = n << 1;
  int right = left | 1;
  tree[left] = suff[left] = -1;
  tree[right] = suff[right] = -1;
  for (a += n, b += n + 1; a < b; a >>= 1, b >>= 1) {
    if (a & 1) pull(left, a++, left);
    if (b & 1) pull(--b, right, right);
  }
  pull(left, right, left);
  return tree[left];
}
int main() {
  scanf("%d%d", &n, &q);
  fill(tree, tree + (n << 1), -1.0);
  fill(suff, suff + (n << 1), -1.0);
  for (int i = 0; i < n; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    update(i, 1.0 * a / b);
  }
  while (q--) {
    int cmd;
    scanf("%d", &cmd);
    if (cmd == 1) {
      int i, a, b;
      scanf("%d%d%d", &i, &a, &b);
      --i;
      update(i, (double)a / b);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      --l, --r;
      printf("%.10lf\n", query(l, r));
    }
  }
}