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 Node {
  double lp, rp;
} a[100500 << 2], ret;
void merge(Node &S, const Node L, const Node R) {
  S.lp = L.lp * R.lp / (1.0 - (1 - R.lp) * L.rp);
  S.rp = R.rp + (1.0 - R.rp) * L.rp * R.lp / (1 - (1 - R.lp) * L.rp);
}
int n, to;
double wfc, p[100500];
void build(int l = 1, int r = n, int u = 1) {
  if (l == r) {
    a[u].lp = a[u].rp = p[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, u << 1);
  build(mid + 1, r, u << 1 | 1);
  merge(a[u], a[u << 1], a[u << 1 | 1]);
}
void chg(int l = 1, int r = n, int u = 1) {
  if (l == r) {
    a[u].lp = a[u].rp = wfc;
    return;
  }
  int mid = (l + r) >> 1;
  if (to <= mid)
    chg(l, mid, u << 1);
  else
    chg(mid + 1, r, u << 1 | 1);
  merge(a[u], a[u << 1], a[u << 1 | 1]);
}
int wfl, wfr;
void qry(int l = 1, int r = n, int u = 1) {
  if (wfl <= l && r <= wfr) {
    if (ret.lp < 0)
      ret = a[u];
    else
      merge(ret, ret, a[u]);
    return;
  }
  int mid = (l + r) >> 1;
  if (wfl <= mid) qry(l, mid, u << 1);
  if (mid < wfr) qry(mid + 1, r, u << 1 | 1);
}
int q;
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1, a, b; i <= n; i++) {
    scanf("%d%d", &a, &b);
    p[i] = 1.0 * a / b;
  }
  build();
  for (int i = 1, op; i <= q; i++) {
    scanf("%d", &op);
    if (op == 1) {
      int a, b;
      scanf("%d%d%d", &to, &a, &b);
      wfc = 1.0 * a / b;
      chg();
    } else {
      scanf("%d%d", &wfl, &wfr);
      ret.lp = -1.0;
      qry();
      printf("%.6lf\n", ret.lp);
    }
  }
  return 0;
}