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 N = 100100;
long double eps = 1e-12;
struct node {
  long double l, r;
} vl[4 * N];
int a[N], b[N], n, q;
int d(long double x) {
  if ((x >= -eps) && (x <= eps)) return 0;
  return 1;
}
node update(node x, node y) {
  if ((d(x.l) == 0) && (d(x.r) == 0)) return y;
  node z;
  z.l = 1 - (1 - x.l) * (1 - y.l) / (1 - x.r * y.l);
  z.r = 1 - (1 - y.r) * (1 - x.r) / (1 - x.r * y.l);
  return z;
}
void build(int l, int r, int rt) {
  if (l == r) {
    vl[rt].r = (long double)a[l] / (long double)b[l];
    vl[rt].l = 1 - vl[rt].r;
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  vl[rt] = update(vl[rt << 1], vl[rt << 1 | 1]);
}
void change(int l, int r, int rt, int pos, long double val) {
  if (l == r) {
    vl[rt].r = val;
    vl[rt].l = 1 - val;
    return;
  }
  int mid = (l + r) >> 1;
  if (pos <= mid)
    change(l, mid, rt << 1, pos, val);
  else
    change(mid + 1, r, rt << 1 | 1, pos, val);
  vl[rt] = update(vl[rt << 1], vl[rt << 1 | 1]);
}
node query(int l, int r, int rt, int ql, int qr) {
  if ((ql <= l) && (r <= qr)) return vl[rt];
  int mid = (l + r) >> 1;
  node res;
  res.l = res.r = 0;
  if (ql <= mid) res = update(res, query(l, mid, rt << 1, ql, qr));
  if (qr > mid) res = update(res, query(mid + 1, r, rt << 1 | 1, ql, qr));
  return res;
}
int main() {
  int i, j, k, x, y, z1, z2;
  double out;
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d%d", &a[i], &b[i]);
  build(1, n, 1);
  while (q--) {
    scanf("%d", &x);
    if (x == 1) {
      scanf("%d%d%d", &y, &z1, &z2);
      change(1, n, 1, y, (long double)z1 / (long double)z2);
    } else {
      scanf("%d%d", &y, &z1);
      out = 1 - (double)query(1, n, 1, y, z1).l;
      printf("%.7f\n", out);
    }
  }
  return 0;
}