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 Prob {
  double l, r;
  bool notset;
  void Merge(Prob a, Prob b) {
    l = a.l * b.l / ((1 - (1 - b.l) * a.r));
    r = b.r + ((1 - b.r) * a.r * b.l) / (1 - (1 - b.l) * a.r);
  }
  void Append(Prob a) {
    if (notset) {
      notset = false;
      *this = a;
      return;
    }
    Prob tmp;
    tmp.Merge(*this, a);
    *this = tmp;
  }
  void init() { notset = true; }
} answ;
struct ST {
  int l, r;
  ST *lc, *rc;
  Prob t;
} t[200009];
int n, q;
double p[100009];
ST* initTree(int l, int r) {
  static int cntT = 0;
  ST* it = &t[cntT++];
  it->l = l, it->r = r;
  if (l == r) {
    it->lc = it->rc = nullptr;
    it->t.l = p[l];
    it->t.r = p[l];
  } else {
    int mid = (l + r) >> 1;
    it->lc = initTree(l, mid);
    it->rc = initTree(mid + 1, r);
    it->t.Merge(it->lc->t, it->rc->t);
  }
  return it;
}
void Update(ST* root, int pos) {
  if (pos < root->l || root->r < pos) return;
  if (root->l == root->r) {
    root->t.l = p[pos];
    root->t.r = p[pos];
  } else {
    Update(root->lc, pos);
    Update(root->rc, pos);
    root->t.Merge(root->lc->t, root->rc->t);
  }
}
void Query(ST* root, int l, int r) {
  if (l <= root->l && root->r <= r) {
    answ.Append(root->t);
  } else {
    if (l <= root->lc->r) Query(root->lc, l, r);
    if (root->rc->l <= r) Query(root->rc, l, r);
  }
}
int main() {
  scanf("%d %d", &n, &q);
  for (int i = 1; i <= n; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    p[i] = a / (double)b;
  }
  ST* root = initTree(1, n);
  int type, l, r, val;
  for (int i = 0; i < q; i++) {
    scanf("%d", &type);
    if (type == 1) {
      scanf("%d %d %d", &val, &l, &r);
      p[val] = l / (double)r;
      Update(root, val);
    } else {
      scanf("%d %d", &l, &r);
      answ.init();
      Query(root, l, r);
      printf("%.11f\n", answ.l);
    }
  }
  return 0;
}