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>
const int N = 100005;
int n, Qi;
double u[N];
namespace SE {
double A[N << 2], B[N << 2];
inline void Up(int t) {
  A[t] = A[t << 1] * A[t << 1 | 1];
  B[t] = B[t << 1] + A[t << 1] * B[t << 1 | 1];
}
void Build(int t, int l, int r) {
  if (l == r) return void(A[t] = B[t] = u[l]);
  int md = (l + r) >> 1;
  Build(t << 1, l, md);
  Build(t << 1 | 1, md + 1, r);
  Up(t);
}
void Modify(int t, int l, int r, int x) {
  if (l == r) return void(A[t] = B[t] = u[l]);
  int md = (l + r) >> 1;
  if (x <= md) Modify(t << 1, l, md, x);
  if (x > md) Modify(t << 1 | 1, md + 1, r, x);
  Up(t);
}
std::pair<double, double> Query(
    int t, int l, int r, int L, int R,
    std::pair<double, double> re = std::make_pair(1, 0)) {
  if (L <= l && r <= R) return std::make_pair(A[t], B[t]);
  int md = (l + r) >> 1;
  if (L <= md) {
    std::pair<double, double> r1 = Query(t << 1, l, md, L, R);
    re = std::make_pair(re.first * r1.first, re.second + re.first * r1.second);
  }
  if (md < R) {
    std::pair<double, double> r2 = Query(t << 1 | 1, md + 1, r, L, R);
    re = std::make_pair(re.first * r2.first, re.second + re.first * r2.second);
  }
  return re;
}
}  // namespace SE
int main() {
  scanf("%d%d", &n, &Qi);
  for (int i = 1, a, b; i <= n; ++i) {
    scanf("%d%d", &a, &b);
    double p = (double)a / b;
    u[i] = (1 - p) / p;
  }
  SE::Build(1, 1, n);
  for (int ty, a, b, x; Qi; --Qi) {
    scanf("%d", &ty);
    if (ty == 1) {
      scanf("%d%d%d", &x, &a, &b);
      double p = (double)a / b;
      u[x] = (1 - p) / p;
      SE::Modify(1, 1, n, x);
    } else {
      scanf("%d%d", &a, &b);
      std::pair<double, double> re = SE::Query(1, 1, n, a, b);
      printf("%.7f\n", 1 / (re.second + 1));
    }
  }
  return 0;
}