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 node {
  double L, R;
  node() {}
  node(double x) : L(x), R(x) {}
  node(double x, double y) : L(x), R(y) {}
  inline node operator+(const node &b) {
    return {L * b.L / (1 - R + R * b.L),
            (R * b.L + b.R - R * b.R) / (1 - R + R * b.L)};
  }
} T[262145];
int N, Q;
void build(int p, int l, int r) {
  if (l == r) {
    int a, b;
    scanf("%d%d", &a, &b);
    T[p] = node(double(a) / b);
  } else {
    int m = l + r >> 1;
    build(p << 1, l, m);
    build(p << 1 | 1, m + 1, r);
    T[p] = T[p << 1] + T[p << 1 | 1];
  }
}
node G(int p, int l, int r, int L, int R) {
  if (L <= l && r <= R) return T[p];
  int m = l + r >> 1;
  if (R <= m) return G(p << 1, l, m, L, R);
  if (L > m) return G(p << 1 | 1, m + 1, r, L, R);
  return G(p << 1, l, m, L, R) + G(p << 1 | 1, m + 1, r, L, R);
}
int main() {
  scanf("%d%d", &N, &Q);
  build(1, 1, N);
  while (Q--) {
    int op, i, a, b;
    scanf("%d", &op);
    if (op == 1) {
      scanf("%d%d%d", &i, &a, &b);
      int p = 1, l = 1, r = N;
      while (l < r) {
        int m = l + r >> 1;
        if (i <= m)
          r = m, p <<= 1;
        else
          l = m + 1, p = p << 1 | 1;
      }
      T[p] = node(double(a) / b);
      while (p > 1) p >>= 1, T[p] = T[p << 1] + T[p << 1 | 1];
    } else {
      scanf("%d%d", &a, &b);
      printf("%.10lf\n", G(1, 1, N, a, b).L);
    }
  }
  return 0;
}