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;
inline int read() {
  int sum = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') ch = getchar();
  while (ch <= '9' && ch >= '0') sum = sum * 10 + ch - '0', ch = getchar();
  return sum;
}
int a[100005], b[100005], n, q;
struct Segment_Tree {
  struct node {
    double sum, Pi;
    node operator+(const node &A) {
      return (node){sum + A.sum * Pi, Pi * A.Pi};
    }
  } t[100005 << 2];
  void update(int x) { t[x] = t[x << 1] + t[x << 1 | 1]; }
  void Build(int x, int l, int r) {
    if (l == r) {
      double p = 1.0 * a[l] / b[l];
      t[x].Pi = t[x].sum = (1.0 - p) / p;
      return;
    }
    int mid = l + r >> 1;
    Build(x << 1, l, mid);
    Build(x << 1 | 1, mid + 1, r);
    update(x);
  }
  void Modify(int x, int l, int r, int val) {
    if (l == r) {
      double p = 1.0 * a[l] / b[l];
      t[x].Pi = t[x].sum = (1.0 - p) / p;
      return;
    }
    int mid = l + r >> 1;
    if (val <= mid)
      Modify(x << 1, l, mid, val);
    else
      Modify(x << 1 | 1, mid + 1, r, val);
    update(x);
  }
  node Query(int x, int l, int r, int L, int R) {
    if (l == L && r == R) return t[x];
    int mid = l + r >> 1;
    if (mid >= R)
      return Query(x << 1, l, mid, L, R);
    else if (mid < L)
      return Query(x << 1 | 1, mid + 1, r, L, R);
    else
      return Query(x << 1, l, mid, L, mid) +
             Query(x << 1 | 1, mid + 1, r, mid + 1, R);
  }
} S;
int main() {
  n = read();
  q = read();
  for (int i = 1; i <= n; ++i) a[i] = read(), b[i] = read();
  S.Build(1, 1, n);
  for (int opt, X, Y, Z, i = 1; i <= q; ++i) {
    opt = read();
    X = read();
    Y = read();
    if (opt == 1) {
      Z = read();
      a[X] = Y;
      b[X] = Z;
      S.Modify(1, 1, n, X);
    } else {
      Segment_Tree::node ans = S.Query(1, 1, n, X, Y);
      ans.sum += 1.0;
      printf("%.10lf\n", 1.0 / ans.sum);
    }
  }
  return 0;
}