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 winLeft, winRight;
  bool empty;
  data() {
    empty = true;
    winLeft = 0;
    winRight = 0;
  }
  data(int p, int q) {
    winLeft = (long double)1.0 * p / q;
    winRight = winLeft;
    empty = false;
  }
};
data merge(data l, data r) {
  if (l.empty && r.empty) return data();
  if (l.empty) return r;
  if (r.empty) return l;
  data res;
  res.empty = false;
  res.winLeft = l.winLeft * r.winLeft / (1 - ((1 - r.winLeft) * l.winRight));
  res.winRight = r.winRight + (1.0 - r.winRight) * l.winRight * r.winLeft /
                                  (1 - ((1 - r.winLeft) * l.winRight));
  return res;
}
struct segmentTree {
  vector<data> tree;
  segmentTree(int n) { tree.resize(4 * n + 17); }
  void change(int v, int tl, int tr, int pos, data val) {
    if (tl == tr) {
      tree[v] = val;
    } else {
      int tm = (tl + tr) / 2;
      if (pos <= tm) {
        change(2 * v, tl, tm, pos, val);
      } else {
        change(2 * v + 1, tm + 1, tr, pos, val);
      }
      tree[v] = merge(tree[2 * v], tree[2 * v + 1]);
    }
  }
  data get(int v, int tl, int tr, int l, int r) {
    if (r < tl || l > tr) return data();
    if (tl >= l && tr <= r) return tree[v];
    int tm = (tl + tr) / 2;
    return merge(get(2 * v, tl, tm, l, r), get(2 * v + 1, tm + 1, tr, l, r));
  }
};
int main() {
  int n, q;
  scanf("%d %d", &n, &q);
  segmentTree st(n + 1);
  for (int i = 1; i <= n; i++) {
    int p, qq;
    scanf("%d %d", &p, &qq);
    st.change(1, 1, n, i, data(p, qq));
  }
  for (int i = 1; i <= q; i++) {
    int type;
    scanf("%d", &type);
    if (type == 1) {
      int pos, p, qq;
      scanf("%d %d %d", &pos, &p, &qq);
      st.change(1, 1, n, pos, data(p, qq));
    } else {
      int l, r;
      scanf("%d %d", &l, &r);
      double res = st.get(1, 1, n, l, r).winLeft;
      printf("%.10lf\n", res);
    }
  }
}