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>
int n, q;
double mul[100010 << 2], ans[100010 << 2], val[100010];
void pushUp(int n) {
  mul[n] = mul[n << 1] * mul[n << 1 | 1];
  ans[n] = ans[n << 1] + mul[n << 1] * ans[n << 1 | 1];
}
void build(int n, int l, int r) {
  if (l == r) {
    mul[n] = ans[n] = (1 - val[l]) / val[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(n << 1, l, mid);
  build(n << 1 | 1, mid + 1, r);
  pushUp(n);
}
void modify(int n, int l, int r, int p) {
  if (l == r) {
    mul[n] = ans[n] = (1 - val[l]) / val[l];
    return;
  }
  int mid = (l + r) >> 1;
  if (p <= mid)
    modify(n << 1, l, mid, p);
  else
    modify(n << 1 | 1, mid + 1, r, p);
  pushUp(n);
}
double Mul, Ans;
void query(int n, int l, int r, int L, int R) {
  if (l == L && r == R) {
    Ans = Ans + Mul * ans[n];
    Mul = Mul * mul[n];
    return;
  }
  int mid = (l + r) >> 1;
  if (R <= mid)
    query(n << 1, l, mid, L, R);
  else if (L > mid)
    query(n << 1 | 1, mid + 1, r, L, R);
  else
    query(n << 1, l, mid, L, mid), query(n << 1 | 1, mid + 1, r, mid + 1, R);
}
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1, x, y; i <= n; i++) {
    scanf("%d%d", &x, &y);
    val[i] = 1. * x / y;
  }
  build(1, 1, n);
  while (q--) {
    int type, l, r, p;
    scanf("%d", &type);
    if (type == 1) {
      scanf("%d%d%d", &p, &l, &r);
      val[p] = 1. * l / r;
      modify(1, 1, n, p);
    } else {
      scanf("%d%d", &l, &r);
      Mul = 1;
      Ans = 0;
      query(1, 1, n, l, r);
      if (Ans <= 1e15)
        printf("%.10lf\n", 1 / (1 + Ans));
      else
        puts("0.0000000000");
    }
  }
  return 0;
}