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 = 100050;
int a[Maxn], b[Maxn], here[Maxn];
class Node {
 public:
  int l, r;
  double f, g;
  Node(int _l = 0, int _r = 0) { l = _l, r = _r; }
} v[Maxn << 2];
Node Merge(Node le, Node ri) {
  Node c = Node(le.l, ri.r);
  c.f = le.f * ri.f / (1 - (1 - ri.f) * le.g);
  c.g = ri.g + (1 - ri.g) * le.g * ri.f / (1 - le.g * (1 - ri.f));
  return c;
}
void push_up(int x) {
  if (x == 0) return;
  int fa = x >> 1;
  if (x & 1) x ^= 1;
  v[fa] = Merge(v[x], v[x ^ 1]);
  push_up(fa);
}
void build(int l, int r, int node) {
  v[node].l = l, v[node].r = r;
  if (l == r) {
    here[l] = node;
    v[node].f = (double)a[l] / b[l], v[node].g = v[node].f;
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, node + node);
  build(mid + 1, r, node + node + 1);
  v[node] = Merge(v[node << 1], v[(node << 1) | 1]);
}
Node ask(int l, int r, int node) {
  if (v[node].l >= l && v[node].r <= r) return v[node];
  Node tmp1, tmp2;
  int flag1 = 0, flag2 = 0, mid = (v[node].l + v[node].r) >> 1;
  if (mid >= l) tmp1 = ask(l, r, node << 1), flag1++;
  if (mid < r) tmp2 = ask(l, r, (node << 1) | 1), flag2++;
  if (flag1 && flag2)
    return Merge(tmp1, tmp2);
  else
    return flag1 ? tmp1 : tmp2;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; ++i) scanf("%d%d", &a[i], &b[i]);
  build(1, n, 1);
  while (q--) {
    int op, l, r;
    scanf("%d%d%d", &op, &l, &r);
    if (op == 1) {
      int t;
      scanf("%d", &t);
      v[here[l]].f = v[here[l]].g = (double)r / t;
      push_up(here[l]);
    } else {
      Node ans = ask(l, r, 1);
      printf("%.10lf\n", ans.f);
    }
  }
}