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 maxn = 100005;
inline int gi() {
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  int sum = 0;
  while ('0' <= c && c <= '9') sum = sum * 10 + c - 48, c = getchar();
  return sum;
}
int n, q;
struct node {
  double l, r;
  node(double _x = 0) { l = r = _x; }
  node(double _l, double _r) {
    l = _l;
    r = _r;
  }
  node operator+(const node &a) const {
    return node(l * a.l / (1 - (1 - a.l) * r),
                a.r + (1 - a.r) * r * a.l / (1 - (1 - a.l) * r));
  }
} t[maxn << 2];
void build(int s, int l, int r) {
  if (l == r) return t[s] = node(1. * gi() / gi()), void();
  build((s << 1), l, ((l + r) >> 1));
  build((s << 1 | 1), ((l + r) >> 1) + 1, r);
  t[s] = t[(s << 1)] + t[(s << 1 | 1)];
}
void modify(int s, int l, int r, int x) {
  if (l == r) return t[s] = node(1. * gi() / gi()), void();
  if (x <= ((l + r) >> 1))
    modify((s << 1), l, ((l + r) >> 1), x);
  else
    modify((s << 1 | 1), ((l + r) >> 1) + 1, r, x);
  t[s] = t[(s << 1)] + t[(s << 1 | 1)];
}
node query(int s, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return t[s];
  if (qr <= ((l + r) >> 1))
    return query((s << 1), l, ((l + r) >> 1), ql, qr);
  else if (ql >= ((l + r) >> 1) + 1)
    return query((s << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
  else
    return query((s << 1), l, ((l + r) >> 1), ql, qr) +
           query((s << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
}
int main() {
  n = gi();
  q = gi();
  build(1, 1, n);
  int op, x, y;
  while (q--) {
    op = gi();
    if (op == 1)
      modify(1, 1, n, gi());
    else
      x = gi(), y = gi(), printf("%.10lf\n", query(1, 1, n, x, y).l);
  }
  return 0;
}