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, q;
double p[100005];
struct fuck {
  double l, r;
} t[100005 * 4], ans;
int read() {
  int x = 0, f = 1;
  char ch;
  for (ch = getchar(); ch < '0' || ch > '9'; ch = getchar())
    if (ch == '-') f = -1;
  for (; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
  return x * f;
}
fuck merge(fuck x, fuck y) {
  return x.l == -1
             ? y
             : (fuck){x.l * y.l / (1 - x.r * (1 - y.l)),
                      y.r + (1 - y.r) * x.r * y.l / (1 - (1 - y.l) * x.r)};
}
void build(int z, int l, int r) {
  if (l == r) {
    t[z].l = t[z].r = p[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(z << 1, l, mid);
  build(z << 1 | 1, mid + 1, r);
  t[z] = merge(t[z << 1], t[z << 1 | 1]);
}
void change(int z, int l, int r, int x, double y) {
  if (l == r) {
    t[z].l = t[z].r = y;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    change(z << 1, l, mid, x, y);
  else
    change(z << 1 | 1, mid + 1, r, x, y);
  t[z] = merge(t[z << 1], t[z << 1 | 1]);
}
void search(int z, int l, int r, int x, int y) {
  if (l >= x && r <= y) {
    ans = merge(ans, t[z]);
    return;
  }
  if (l > y || r < x) return;
  int mid = (l + r) >> 1;
  search(z << 1, l, mid, x, y);
  search(z << 1 | 1, mid + 1, r, x, y);
}
int main() {
  n = read();
  q = read();
  for (int i = 1, a, b; i <= n; i++) {
    a = read();
    b = read();
    p[i] = 1.0 * a / b;
  }
  build(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int op = read();
    if (op == 1) {
      int x = read(), a = read(), b = read();
      change(1, 1, n, x, 1.0 * a / b);
    } else {
      int x = read(), y = read();
      ans.l = ans.r = -1;
      search(1, 1, n, x, y);
      printf("%.6lf\n", ans.l);
    }
  }
  return 0;
}