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;
inline int readint() {
  int a = 0;
  char c = getchar(), f = 1;
  for (; c < '0' || c > '9'; c = getchar())
    if (c == '-') f = -f;
  for (; '0' <= c && c <= '9'; c = getchar())
    a = (a << 3) + (a << 1) + (c ^ 48);
  return a * f;
}
struct Node {
  double l, r;
  Node() {}
  Node(double L, double R) : l(L), r(R) {}
};
Node operator+(const Node &a, const Node &b) {
  return Node(a.l + (1 - a.l) * (1 - a.r) * b.l / (1 - a.r * b.l),
              b.r + (1 - b.r) * (1 - b.l) * a.r / (1 - a.r * b.l));
}
const int MaxN = 100005;
Node val[MaxN << 1];
int n;
void modify(int qid, double v, int l = 1, int r = n) {
  if (l == r) {
    val[l << 1].l = 1 - v;
    val[l << 1].r = v;
    return;
  }
  int mid = (l + r) >> 1;
  if (mid < qid)
    modify(qid, v, mid + 1, r);
  else
    modify(qid, v, l, mid);
  val[(((l) + (r)) | ((l) != (r)))] =
      val[(((l) + (mid)) | ((l) != (mid)))] +
      val[(((mid + 1) + (r)) | ((mid + 1) != (r)))];
}
Node query(int ql, int qr, int l = 1, int r = n) {
  if (ql <= l && r <= qr) return val[(((l) + (r)) | ((l) != (r)))];
  int mid = (l + r) >> 1;
  if (qr <= mid) return query(ql, qr, l, mid);
  if (mid < ql) return query(ql, qr, mid + 1, r);
  return query(ql, qr, l, mid) + query(ql, qr, mid + 1, r);
}
int main() {
  n = readint();
  int q = readint();
  for (int i = 1, a, b; i <= n; ++i) {
    a = readint(), b = readint();
    modify(i, 1.0 * a / b);
  }
  for (int opt, a, b, x; q; --q) {
    opt = readint();
    if (opt == 1) x = readint();
    a = readint(), b = readint();
    if (opt == 1) modify(x, 1.0 * a / b);
    if (opt == 2) printf("%.10f\n", 1 - query(a, b).l);
  }
  return 0;
}