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;
int n, q;
double p[100005];
struct dot {
  double a, b, c, d;
  dot(double _a = 0, double _b = 0) { a = _a, b = _b; }
} A[4 * 100005];
dot update(dot p, dot q) {
  dot r;
  r.a = (p.a * q.a) / (1 - p.b * (1 - q.a));
  r.b = q.b + ((1 - q.b) * p.b * q.a) / (1 - p.b * (1 - q.a));
  return r;
}
void build(int t, int l, int r) {
  int mid = (l + r) >> 1;
  if (l == r) {
    A[t].a = A[t].b = p[l];
    return;
  }
  build((t << 1), l, mid);
  build(((t << 1) | 1), mid + 1, r);
  A[t] = update(A[(t << 1)], A[((t << 1) | 1)]);
}
dot query(int t, int l, int r, int l1, int r1) {
  int mid = (l + r) >> 1;
  dot p, q;
  if (l >= l1 && r <= r1) return A[t];
  if (r1 <= mid) return query((t << 1), l, mid, l1, r1);
  if (l1 > mid) return query(((t << 1) | 1), mid + 1, r, l1, r1);
  p = query((t << 1), l, mid, l1, r1);
  q = query(((t << 1) | 1), mid + 1, r, l1, r1);
  p = update(p, q);
  return p;
}
void modify(int t, int l, int r, int s) {
  int mid = (l + r) >> 1;
  if (l == r) {
    A[t].a = A[t].b = p[l];
    return;
  }
  if (s <= mid)
    modify((t << 1), l, mid, s);
  else
    modify(((t << 1) | 1), mid + 1, r, s);
  A[t] = update(A[(t << 1)], A[((t << 1) | 1)]);
}
int main() {
  int i, x, y, op, l, r;
  scanf("%d %d", &n, &q);
  for (i = 1; i <= n; i++) {
    scanf("%d %d", &x, &y);
    p[i] = 1.0 * x / y;
  }
  build(1, 1, n);
  while (q--) {
    scanf("%d ", &op);
    if (op == 2) {
      scanf("%d %d", &l, &r);
      dot tmp = query(1, 1, n, l, r);
      printf("%.8lf\n", tmp.a);
    } else {
      scanf("%d %d %d", &l, &x, &y);
      p[l] = 1.0 * x / y;
      modify(1, 1, n, l);
    }
  }
  return 0;
}