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;
const int maxn = 1e5 + 15;
const int mod = 1e9 + 7;
const int inf = 0x3f3f3f3f;
int n, m;
double a[maxn * 4], b[maxn * 4];
double q[maxn * 4];
inline void push_up(int u) {
  a[u] = a[(u << 1)] * a[(u << 1 | 1)];
  b[u] = b[(u << 1)] + b[(u << 1 | 1)] * a[(u << 1)];
}
void build(int u, int l, int r) {
  if (l == r) {
    a[u] = q[l];
    b[u] = q[l];
    return;
  }
  int mid = (l + r) >> 1;
  build((u << 1), l, mid);
  build((u << 1 | 1), mid + 1, r);
  push_up(u);
}
void upd(int u, int l, int r, int x, double cc) {
  if (l == r) {
    a[u] = b[u] = cc;
    return;
  }
  int mid = (l + r) >> 1;
  if (x <= mid)
    upd((u << 1), l, mid, x, cc);
  else
    upd((u << 1 | 1), mid + 1, r, x, cc);
  push_up(u);
}
pair<double, double> query(int u, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) {
    return make_pair(a[u], b[u]);
  }
  int mid = (l + r) >> 1;
  if (qr <= mid)
    return query((u << 1), l, mid, ql, qr);
  else if (ql > mid)
    return query((u << 1 | 1), mid + 1, r, ql, qr);
  else {
    pair<double, double> lef = query((u << 1), l, mid, ql, qr);
    pair<double, double> rig = query((u << 1 | 1), mid + 1, r, ql, qr);
    pair<double, double> ret;
    ret.second = lef.second + rig.second * lef.first;
    ret.first = lef.first * rig.first;
    return ret;
  }
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1, a, b; i <= n; i++) {
    scanf("%d%d", &a, &b);
    double pp = double(a) / b;
    q[i] = (1 - pp) / pp;
  }
  build(1, 1, n);
  while (m--) {
    int op, x, y, z;
    scanf("%d", &op);
    if (op == 1) {
      scanf("%d%d%d", &x, &y, &z);
      double pp = double(y) / z;
      q[x] = (1 - pp) / pp;
      upd(1, 1, n, x, q[x]);
    } else {
      scanf("%d%d", &x, &y);
      printf("%.10f\n", 1.0 / (query(1, 1, n, x, y).second + 1));
    }
  }
  return 0;
}