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 node {
  int l, r;
  double tl, tr;
} t[100050 * 4];
node merge(node A, node B) {
  node C;
  C.l = A.l;
  C.r = B.r;
  C.tl = A.tl * B.tl / (1 - (1 - B.tl) * (1 - A.tr));
  C.tr = A.tr * B.tr / (1 - (1 - B.tl) * (1 - A.tr));
  return C;
}
double p[100050];
void build(int x, int l, int r) {
  t[x].l = l;
  t[x].r = r;
  if (l == r) {
    t[x].tl = p[l];
    t[x].tr = 1 - p[l];
    return;
  }
  int mid = l + r >> 1;
  build((x << 1), l, mid);
  build(((x << 1) | 1), mid + 1, r);
  t[x] = merge(t[(x << 1)], t[((x << 1) | 1)]);
}
void update(int x, int pos, double val) {
  if (t[x].l == t[x].r) {
    t[x].tl = val;
    t[x].tr = 1 - val;
    return;
  }
  int mid = (t[x].l + t[x].r) >> 1;
  if (pos <= mid)
    update((x << 1), pos, val);
  else
    update(((x << 1) | 1), pos, val);
  t[x] = merge(t[(x << 1)], t[((x << 1) | 1)]);
}
node query(int x, int L, int R) {
  if (L <= t[x].l && t[x].r <= R) return t[x];
  int mid = (t[x].l + t[x].r) >> 1;
  if (R <= mid)
    return query((x << 1), L, R);
  else if (L > mid)
    return query(((x << 1) | 1), L, R);
  else
    return merge(query((x << 1), L, R), query(((x << 1) | 1), L, R));
}
int n, q;
int main() {
  double x, y;
  int opt, d, l, r;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; ++i) {
    scanf("%lf%lf", &x, &y);
    p[i] = x / y;
  }
  build(1, 1, n);
  while (q--) {
    scanf("%d", &opt);
    if (opt == 1) {
      scanf("%d%lf%lf", &d, &x, &y);
      update(1, d, x / y);
    } else {
      scanf("%d%d", &l, &r);
      printf("%.8lf\n", query(1, l, r).tl);
      fflush(stdout);
    }
  }
  return 0;
}