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;
struct data {
  long double ll, lr, rl, rr;
} a[100010 << 2];
long double R[100010], L[100010];
int x, y, n, m, i, op;
data mer(data x, data y, long double p1, long double p2) {
  data t =
      (data){x.lr * x.rl * y.ll * p1 * p2 / (1 - p1 * p2 * x.rr * y.ll) + x.ll,
             x.lr * y.lr * p1 / (1 - p1 * p2 * x.rr * y.ll),
             x.rl * y.rl * p2 / (1 - p1 * p2 * x.rr * y.ll),
             y.rl * y.lr * x.rr * p1 * p2 / (1 - p1 * p2 * x.rr * y.ll) + y.rr};
  return t;
}
void up(int t, int l, int r, int x) {
  if (l == r)
    a[t] = (data){1, 1, 1, 1};
  else
    x <= ((l + r) >> 1) ? up(t << 1, l, ((l + r) >> 1), x)
                        : up(t << 1 | 1, ((l + r) >> 1) + 1, r, x),
        a[t] = mer(a[t << 1], a[t << 1 | 1], R[((l + r) >> 1)],
                   L[((l + r) >> 1) + 1]);
}
data ask(int t, int l, int r) {
  if (x <= l && r <= y) return a[t];
  if (y <= ((l + r) >> 1)) return ask(t << 1, l, ((l + r) >> 1));
  if (x > ((l + r) >> 1)) return ask(t << 1 | 1, ((l + r) >> 1) + 1, r);
  return mer(ask(t << 1, l, ((l + r) >> 1)),
             ask(t << 1 | 1, ((l + r) >> 1) + 1, r), R[((l + r) >> 1)],
             L[((l + r) >> 1) + 1]);
}
int rd() {
  int t;
  scanf("%d", &t);
  return t;
}
int main() {
  n = rd(), m = rd();
  for (i = 1; i <= n; i++)
    x = rd(), y = rd(), R[i] = (long double)x / y, L[i] = 1 - R[i];
  for (i = 1; i <= n; i++) up(1, 1, n, i);
  for (i = 1; i <= m; i++) {
    op = rd();
    if (op - 1)
      x = rd(), y = rd(), cout << ask(1, 1, n).lr * R[y] << "\n";
    else
      op = rd(), x = rd(), y = rd(), R[op] = (long double)x / y,
      L[op] = 1 - R[op], up(1, 1, n, op);
  }
  return 0;
}