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 = 110000;
int n, q;
double s, ans, t[maxn * 4], mul[maxn * 4], val[maxn * 4];
void update(int pos) {
  val[pos] = val[pos + pos] + mul[pos + pos] * val[pos + pos + 1];
  mul[pos] = mul[pos + pos] * mul[pos + pos + 1];
}
void build(int pos, int x, int y) {
  if (x == y) {
    mul[pos] = val[pos] = t[x];
    return;
  }
  int mid = (x + y) / 2;
  build(pos + pos, x, mid);
  build(pos + pos + 1, mid + 1, y);
  update(pos);
}
void modify(int pos, int x, int y, int id) {
  if (x == y) {
    mul[pos] = val[pos] = t[y];
    return;
  }
  int mid = (x + y) / 2;
  if (id <= mid)
    modify(pos + pos, x, mid, id);
  else
    modify(pos + pos + 1, mid + 1, y, id);
  update(pos);
}
void query(int pos, int x, int y, int xx, int yy) {
  if (x == xx && y == yy) {
    ans += s * val[pos];
    s *= mul[pos];
    return;
  }
  int mid = (x + y) / 2;
  if (yy <= mid)
    query(pos + pos, x, mid, xx, yy);
  else if (xx > mid)
    query(pos + pos + 1, mid + 1, y, xx, yy);
  else {
    query(pos + pos, x, mid, xx, mid);
    query(pos + pos + 1, mid + 1, y, mid + 1, yy);
  }
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    t[i] = 1.0 * (b - a) / a;
  }
  build(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int tp;
    scanf("%d", &tp);
    if (tp == 1) {
      int p, a, b;
      scanf("%d%d%d", &p, &a, &b);
      t[p] = 1.0 * (b - a) / a;
      modify(1, 1, n, p);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      ans = 0;
      s = 1;
      query(1, 1, n, l, r);
      ans = 1 / (ans + 1);
      if (ans >= 0 && ans <= 1)
        printf("%.6lf\n", ans);
      else
        printf("0.000000\n");
    }
  }
  return 0;
}