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 NMAX = 270000;
struct Node {
  double LL, LR, RL, RR;
};
int N, Q;
int L;
Node tree[NMAX];
Node merge(const Node &l, const Node &r) {
  double t1, t2;
  t1 = l.LL + l.LR * r.LL * l.RL * 1 / (1 - l.RR * r.LL);
  t2 = r.RR + r.RL * l.RR * r.LR * 1 / (1 - r.LL * l.RR);
  return (Node){t1, 1 - t1, 1 - t2, t2};
}
void buildTree() {
  int pos;
  for (pos = L - 1; pos; pos -= 1)
    tree[pos] = merge(tree[2 * pos], tree[2 * pos + 1]);
}
void edit(int pos, double v) {
  pos += L - 1;
  tree[pos] = (Node){1 - v, v, 1 - v, v};
  for (pos >>= 1; pos; pos >>= 1)
    tree[pos] = merge(tree[2 * pos], tree[2 * pos + 1]);
}
Node query(int pos, int l, int r, int p, int q) {
  int mid = (l + r) >> 1;
  Node resl, resr;
  if (l == p && r == q) return tree[pos];
  if (p <= mid) resl = query(2 * pos, l, mid, p, min(q, mid));
  if (q > mid) resr = query(2 * pos + 1, mid + 1, r, max(p, mid + 1), q);
  if (p <= mid && q > mid)
    return merge(resl, resr);
  else if (p <= mid)
    return resl;
  return resr;
}
int main() {
  int i, t, pos, x, y;
  scanf("%d %d", &N, &Q);
  for (L = 1; L < N; L <<= 1)
    ;
  for (i = 1; i <= N; i += 1) {
    scanf("%d %d", &x, &y);
    tree[L + i - 1] = (Node){1 - (double)x / y, (double)x / y,
                             1 - (double)x / y, (double)x / y};
  }
  for (; i <= L; i += 1) tree[L + i - 1] = (Node){0.5, 0.5, 0.5, 0.5};
  buildTree();
  for (i = 1; i <= Q; i += 1) {
    scanf("%d", &t);
    if (t == 1) {
      scanf("%d %d %d", &pos, &x, &y);
      edit(pos, (double)x / y);
    } else {
      scanf("%d %d", &x, &y);
      printf("%.10f\n", query(1, 1, L, x, y).LR);
    }
  }
  exit(0);
}