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>
#pragma comment(linker, "/STACK: 1024000000,1024000000")
using namespace std;
inline int getint() {
  int _x = 0;
  char _tc = getchar();
  while (_tc < '0' || _tc > '9') _tc = getchar();
  while (_tc >= '0' && _tc <= '9') _x *= 10, _x += (_tc - '0'), _tc = getchar();
  return _x;
}
pair<double, double> tp = make_pair(1.0, 0);
const int N = 1e5 + 15;
double a[N * 4], b[N * 4];
void up(int rt) {
  a[rt] = a[rt << 1] * a[rt << 1 | 1];
  b[rt] = b[rt << 1] + b[rt << 1 | 1] * a[rt << 1];
}
void upd(int rt, int l, int r, int L, int R, pair<double, double> v) {
  if (L <= l && r <= R) {
    a[rt] = v.first;
    b[rt] = v.second;
    return;
  }
  int mid = l + r >> 1;
  if (L <= mid) upd(rt << 1, l, mid, L, R, v);
  if (R > mid) upd(rt << 1 | 1, mid + 1, r, L, R, v);
  up(rt);
}
pair<double, double> qry(int rt, int l, int r, int L, int R) {
  if (L <= l && r <= R) return make_pair(a[rt], b[rt]);
  int mid = l + r >> 1;
  pair<double, double> aa = tp, bb = tp, cc;
  if (L <= mid) aa = qry(rt << 1, l, mid, L, R);
  if (R > mid) bb = qry(rt << 1 | 1, mid + 1, r, L, R);
  up(rt);
  cc.first = aa.first * bb.first;
  cc.second = aa.second + bb.second * aa.first;
  return cc;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) {
    double x, y;
    scanf("%lf%lf", &x, &y);
    double p = x / y;
    double pp = (1.0 - p) / p;
    upd(1, 1, n, i, i, make_pair(pp, pp));
  }
  for (int i = 1; i <= q; i++) {
    int op, aa, bb, cc;
    scanf("%d", &op);
    if (op == 1) {
      scanf("%d%d%d", &aa, &bb, &cc);
      double p = 1.0 * bb / cc;
      double pp = (1.0 - p) / p;
      upd(1, 1, n, aa, aa, make_pair(pp, pp));
    } else {
      scanf("%d%d", &aa, &bb);
      double p = qry(1, 1, n, aa, bb).second;
      if (p < 1e20)
        printf("%.12f\n", 1.0 / (1.0 + p));
      else
        puts("0.000000000000");
    }
  }
  return 0;
}