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;
int n, m;
double sum[400010], ans[400010];
void build(int p, int l, int r) {
  if (l == r) {
    ans[p] = 2;
    sum[p] = 1;
    return;
  }
  int mid = (l + r) >> 1;
  build(p << 1, l, mid);
  build(p << 1 | 1, mid + 1, r);
  sum[p] = min(1e9, sum[p << 1] * sum[p << 1 | 1]);
  ans[p] = min(1e9, ans[p << 1] + sum[p << 1] * (ans[p << 1 | 1] - 1));
}
void update(int p, int l, int r, int x, double z) {
  if (l == r) {
    ans[p] = z + 1;
    sum[p] = z;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    update(p << 1, l, mid, x, z);
  else
    update(p << 1 | 1, mid + 1, r, x, z);
  sum[p] = min(1e9, sum[p << 1] * sum[p << 1 | 1]);
  ans[p] = min(1e9, ans[p << 1] + sum[p << 1] * (ans[p << 1 | 1] - 1));
}
struct qq {
  double as, sum;
};
qq ask(int p, int l, int r, int x, int y) {
  int mid = (l + r) >> 1;
  if (x <= l && y >= r) return (qq){ans[p], sum[p]};
  if (y <= mid) return ask(p << 1, l, mid, x, y);
  if (x > mid) return ask(p << 1 | 1, mid + 1, r, x, y);
  qq t = ask(p << 1, l, mid, x, y), t2 = ask(p << 1 | 1, mid + 1, r, x, y);
  return (qq){min(1e9, t.as + t.sum * (t2.as - 1)), min(t.sum * t2.sum, 1e9)};
}
int main() {
  scanf("%d%d", &n, &m);
  build(1, 1, n);
  for (int i = 1, a, b; i <= n; i++)
    scanf("%d%d", &a, &b), update(1, 1, n, i, 1.0 * (b - a) / a);
  for (int i = 1, ty, l, r, a, b, x; i <= m; i++) {
    scanf("%d", &ty);
    if (ty & 1)
      scanf("%d%d%d", &x, &a, &b), update(1, 1, n, x, 1.0 * (b - a) / a);
    else
      scanf("%d%d", &l, &r), printf("%.6lf\n", 1.0 / ask(1, 1, n, l, r).as);
  }
  return 0;
}