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 = 1e5 + 10;
int N, Q;
struct Node {
  double f, g;
} t[MAXN << 2];
Node pushup(Node t1, Node t2) {
  double &f1 = t1.f, &g1 = t1.g;
  double &f2 = t2.f, &g2 = t2.g;
  double f = f1 * f2 / (1 - (1 - f2) * g1);
  double g = g2 + (1 - g2) * g1 * f2 / (1 + (f2 - 1) * g1);
  return {f, g};
}
void update(int root, int pos, double val, int L = 1, int R = N) {
  if (L == R) return void(t[root].f = t[root].g = val);
  int mid = L + (R - L) / 2;
  if (pos <= mid)
    update(root * 2, pos, val, L, mid);
  else
    update(root * 2 + 1, pos, val, mid + 1, R);
  t[root] = pushup(t[root * 2], t[root * 2 + 1]);
}
Node query(int root, int a, int b, int L = 1, int R = N) {
  if (a == L && b == R) return t[root];
  int mid = L + (R - L) / 2;
  if (b <= mid)
    return query(root * 2, a, b, L, mid);
  else if (a > mid)
    return query(root * 2 + 1, a, b, mid + 1, R);
  else {
    return pushup(query(root * 2, a, mid, L, mid),
                  query(root * 2 + 1, mid + 1, b, mid + 1, R));
  }
}
int main() {
  scanf("%d%d", &N, &Q);
  for (int i = 1; i <= N; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    update(1, i, a * 1.0 / b);
  }
  while (Q--) {
    int op;
    scanf("%d", &op);
    if (op == 1) {
      int pos, a, b;
      scanf("%d%d%d", &pos, &a, &b);
      update(1, pos, a * 1.0 / b);
    } else {
      int a, b;
      scanf("%d%d", &a, &b);
      printf("%.10f\n", query(1, a, b).f);
    }
  }
  return 0;
}