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 nd {
  double l, r;
} t[500000];
double p[500000];
int n, q;
nd Update(nd a, nd b) {
  if ((a.l + 1 == 0) && (a.r + 1 == 0)) return b;
  if ((b.l + 1 == 0) && (b.r + 1 == 0)) return a;
  nd ret;
  ret.l = ret.r = 0;
  double l1 = a.l, l2 = b.l, r1 = a.r, r2 = b.r;
  if ((1 - r1 * (1 - l2)) == 0) return ret;
  ret.l = l1 * l2 / (1 - r1 * (1 - l2));
  ret.r = r2 + r1 * l2 * (1 - r2) / (1 - r1 * (1 - l2));
  return ret;
}
void build(int n, int l, int r) {
  if (l == r) {
    t[n].l = t[n].r = p[l];
    return;
  }
  int mid = (l + r) / 2;
  build(n * 2, l, mid), build(n * 2 + 1, mid + 1, r);
  t[n] = Update(t[n * 2], t[n * 2 + 1]);
}
void Change(int n, int l, int r, int x, double p) {
  if (l == r) {
    t[n].l = t[n].r = p;
    return;
  }
  int mid = (l + r) / 2;
  if (x <= mid)
    Change(n * 2, l, mid, x, p);
  else
    Change(n * 2 + 1, mid + 1, r, x, p);
  t[n] = Update(t[n * 2], t[n * 2 + 1]);
}
nd Ask(int n, int l, int r, int ql, int qr) {
  nd ret;
  if ((ql > r) || (qr < l)) {
    ret.l = ret.r = -1;
    return ret;
  }
  if ((ql <= l) && (qr >= r)) return t[n];
  int mid = (l + r) / 2;
  return Update(Ask(n * 2, l, mid, ql, qr), Ask(n * 2 + 1, mid + 1, r, ql, qr));
}
int main() {
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    p[i] = (double)a / b;
  }
  build(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int op;
    scanf("%d", &op);
    if (op == 1) {
      int x, a, b;
      scanf("%d%d%d", &x, &a, &b);
      double p = (double)a / b;
      Change(1, 1, n, x, p);
    } else {
      nd ret;
      int l, r;
      scanf("%d%d", &l, &r);
      ret = Ask(1, 1, n, l, r);
      printf("%.10f\n", ret.l);
    }
  }
}