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>
const int maxn = 100010;
int a[maxn], b[maxn];
std::pair<double, double> value[maxn << 2];
using Node = std::pair<double, double>;
Node merge(Node childL, Node childR) {
  double l1, r1, l2, r2;
  std::tie(l1, r1) = childL;
  std::tie(l2, r2) = childR;
  double l = l1 * l2 / (1 + r1 * (l2 - 1));
  double r = r2 + (r1 * l2 * (1 - r2)) / (1 + r1 * (l2 - 1));
  return std::make_pair(l, r);
}
void update(int o, int l, int r, int begin, int end, double value) {
  if (begin == l && end == r) {
    ::value[o] = std::make_pair(value, value);
    return;
  }
  int m = (l + r) >> 1;
  if (end <= m) {
    update(o * 2, l, m, begin, end, value);
  }
  if (begin > m) {
    update(o * 2 + 1, m + 1, r, begin, end, value);
  }
  ::value[o] = merge(::value[o * 2], ::value[o * 2 + 1]);
}
Node query(int o, int l, int r, int begin, int end) {
  if (begin > r || end < l) {
    return std::make_pair(1.0, 0.0);
  }
  if (l >= begin && r <= end) {
    return value[o];
  }
  auto resultL = std::make_pair(1.0, 0.0);
  auto resultR = std::make_pair(1.0, 0.0);
  int m = (l + r) >> 1;
  resultL = query(o * 2, l, m, begin, end);
  resultR = query(o * 2 + 1, m + 1, r, begin, end);
  return merge(resultL, resultR);
}
int main() {
  int n, q;
  std::cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    std::cin >> a[i] >> b[i];
    update(1, 1, n, i, i, a[i] * 1.0 / b[i]);
  }
  for (int i = 0; i < q; i++) {
    int oper;
    std::cin >> oper;
    if (oper == 1) {
      int index, a, b;
      std::cin >> index >> a >> b;
      update(1, 1, n, index, index, a * 1.0 / b);
    } else {
      int l, r;
      std::cin >> l >> r;
      std::cout << std::fixed << std::setprecision(9)
                << query(1, 1, n, l, r).first << std::endl;
    }
  }
  return 0;
}