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;
struct node {
  int l, r;
  double A, B;
} T[100010 << 2];
double num[100010];
inline void pushup(int rt) {
  T[rt].A = T[rt << 1].A * T[rt << 1 | 1].A;
  T[rt].B = T[rt << 1].B + T[rt << 1].A * T[rt << 1 | 1].B;
}
void build(int rt, int l, int r) {
  T[rt].l = l, T[rt].r = r;
  int mid = (l + r) >> 1;
  if (l == r) {
    T[rt].A = T[rt].B = num[l];
    return;
  }
  build(rt << 1, l, mid), build(rt << 1 | 1, mid + 1, r);
  pushup(rt);
}
void update(int rt, int at, double x) {
  int l = T[rt].l, r = T[rt].r, mid = (l + r) >> 1;
  if (l == r) {
    T[rt].A = T[rt].B = x;
    return;
  }
  if (at <= mid)
    update(rt << 1, at, x);
  else
    update(rt << 1 | 1, at, x);
  pushup(rt);
}
pair<double, double> query(int rt, int start, int end) {
  int l = T[rt].l, r = T[rt].r, mid = (l + r) >> 1;
  if (start <= l && r <= end) return make_pair(T[rt].A, T[rt].B);
  if (end <= mid) return query(rt << 1, start, end);
  if (start > mid) return query(rt << 1 | 1, start, end);
  pair<double, double> tmp1 = query(rt << 1, start, end),
                       tmp2 = query(rt << 1 | 1, start, end);
  return make_pair(tmp1.first * tmp2.first,
                   tmp1.second + tmp1.first * tmp2.second);
}
int main() {
  int n, q, a, b;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++)
    scanf("%d%d", &a, &b), num[i] = (double)(b - a) / a;
  build(1, 1, n);
  while (q--) {
    int op, c;
    scanf("%d%d%d", &op, &a, &b);
    if (op == 1)
      scanf("%d", &c), update(1, a, (double)(c - b) / b);
    else
      printf("%.10lf\n", 1 / (1 + query(1, a, b).second));
  }
  return 0;
}