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>
struct Node {
  double pl, pr;
};
const int MAXN = 100000 + 10;
Node pst[MAXN * 3];
int n;
void update(int o, int l, int r, double v, int p) {
  if (l == r) {
    pst[o].pl = pst[o].pr = v;
    return;
  }
  int m = (l + r) / 2;
  if (p <= m)
    update(o * 2, l, m, v, p);
  else
    update(o * 2 + 1, m + 1, r, v, p);
  double l1 = pst[o * 2].pl, r1 = pst[o * 2].pr, l2 = pst[o * 2 + 1].pl,
         r2 = pst[o * 2 + 1].pr;
  pst[o].pl = l1 * l2 / (1 + r1 * (l2 - 1));
  pst[o].pr = r2 + r1 * l2 * (1 - r2) / (1 - r1 * (1 - l2));
}
Node query(int o, int l, int r, int ql, int qr) {
  int m = (l + r) / 2;
  if (ql <= l && r <= qr) return pst[o];
  Node ans;
  ans.pl = 1;
  ans.pr = 0;
  if (ql <= m) {
    Node tmp = query(o * 2, l, m, ql, qr);
    double l1 = ans.pl, r1 = ans.pr, l2 = tmp.pl, r2 = tmp.pr;
    ans.pl = l1 * l2 / (1 + r1 * (l2 - 1));
    ans.pr = r2 + r1 * l2 * (1 - r2) / (1 - r1 * (1 - l2));
  }
  if (m < qr) {
    Node tmp = query(o * 2 + 1, m + 1, r, ql, qr);
    double l1 = ans.pl, r1 = ans.pr, l2 = tmp.pl, r2 = tmp.pr;
    ans.pl = l1 * l2 / (1 + r1 * (l2 - 1));
    ans.pr = r2 + r1 * l2 * (1 - r2) / (1 - r1 * (1 - l2));
  }
  return ans;
}
int main() {
  int q, code;
  int tmp, l, r;
  scanf("%d%d", &n, &q);
  double a, b;
  for (int i = 1; i <= n; i++) {
    scanf("%lf %lf", &a, &b);
    update(1, 1, n, a / b, i);
  }
  while (q--) {
    scanf("%d", &code);
    if (code == 1) {
      scanf("%d %lf %lf", &tmp, &a, &b);
      update(1, 1, n, a / b, tmp);
    } else {
      scanf("%d%d", &l, &r);
      Node ans = query(1, 1, n, l, r);
      printf("%.10lf\n", ans.pl);
    }
  }
  return 0;
}