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>
struct treenode {
  double L, R;
};
treenode tree[500000];
int i, m, n, t, x, y, z;
inline treenode merge(treenode l, treenode r) {
  return (treenode){l.L + (1 - l.L) * r.L * (1 - l.R) / (1 - r.L * l.R),
                    r.R + (1 - r.R) * l.R * (1 - r.L) / (1 - r.L * l.R)};
}
inline void buildtree(int l, int r, int node) {
  if (l == r) {
    scanf("%d%d", &x, &y);
    tree[node].L = 1 - 1.0 * x / y;
    tree[node].R = 1.0 * x / y;
  } else {
    int mid = (l + r) >> 1;
    buildtree(l, mid, node << 1);
    buildtree(mid + 1, r, node << 1 | 1);
    tree[node] = merge(tree[node << 1], tree[node << 1 | 1]);
  }
  return;
}
inline void inserttree(int l, int r, int x, int y, int z, int node) {
  if (l == r) {
    tree[node].L = 1 - 1.0 * y / z;
    tree[node].R = 1.0 * y / z;
  } else {
    int mid = (l + r) >> 1;
    if (x <= mid)
      inserttree(l, mid, x, y, z, node << 1);
    else
      inserttree(mid + 1, r, x, y, z, node << 1 | 1);
    tree[node] = merge(tree[node << 1], tree[node << 1 | 1]);
  }
  return;
}
inline treenode asktree(int l, int r, int x, int y, int node) {
  if ((l == x) && (r == y)) return tree[node];
  int mid = (l + r) >> 1;
  if (y <= mid) return asktree(l, mid, x, y, node << 1);
  if (x > mid) return asktree(mid + 1, r, x, y, node << 1 | 1);
  return merge(asktree(l, mid, x, mid, node << 1),
               asktree(mid + 1, r, mid + 1, y, node << 1 | 1));
}
int main() {
  scanf("%d%d", &n, &m);
  buildtree(1, n, 1);
  for (i = 1; i <= m; i++) {
    scanf("%d", &t);
    if (t == 1) {
      scanf("%d%d%d", &x, &y, &z);
      inserttree(1, n, x, y, z, 1);
    } else {
      scanf("%d%d", &x, &y);
      printf("%.10lf\n", 1 - asktree(1, n, x, y, 1).L);
    }
  }
  return 0;
}