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 double eps = 1e-7;
struct node {
  double l, r;
  node(double lr = 0.0, double rr = 0.0) : l(lr), r(rr) {}
} st[100034 << 2];
int n, q;
double readDouble() {
  int a, b;
  scanf("%d%d", &a, &b);
  return (double)a / (double)b;
}
node merge(const node l, const node r) {
  node ret;
  double D = 1.0 - (1.0 - r.l) * l.r;
  if (D < eps) {
    ret.l = 0.0;
    ret.r = r.r;
  } else {
    ret.l = l.l * r.l / D;
    ret.r = r.r + l.r * r.l * (1.0 - r.r) / D;
  }
  return ret;
}
void build(int id, int L, int R) {
  if (L == R) {
    double p = readDouble();
    st[id] = node(p, p);
    return;
  }
  int M = (L + R - 1) >> 1, lc = id << 1, rc = lc | 1;
  build(lc, L, M);
  build(rc, M + 1, R);
  st[id] = merge(st[lc], st[rc]);
}
void adj(int id, int L, int R, int h, double v) {
  if (L == R) {
    st[id] = node(v, v);
    return;
  }
  int M = (L + R - 1) >> 1, lc = id << 1, rc = lc | 1;
  h <= M ? adj(lc, L, M, h, v) : adj(rc, M + 1, R, h, v);
  st[id] = merge(st[lc], st[rc]);
}
node range(int id, int L, int R, int ql, int qr) {
  if (ql <= L && R <= qr) return st[id];
  int M = (L + R - 1) >> 1, lc = id << 1, rc = lc | 1;
  node ret;
  if (ql <= M) {
    ret = range(lc, L, M, ql, min(qr, M));
    if (qr > M) ret = merge(ret, range(rc, M + 1, R, max(ql, M + 1), qr));
  } else if (qr > M)
    ret = range(rc, M + 1, R, max(ql, M + 1), qr);
  return ret;
}
int main() {
  int op, u, v;
  double p;
  scanf("%d%d", &n, &q);
  build(1, 1, n);
  for (; q; --q)
    if (scanf("%d", &op), op == 1) {
      scanf("%d", &v);
      p = readDouble();
      adj(1, 1, n, v, p);
    } else {
      scanf("%d%d", &u, &v);
      p = range(1, 1, n, u, v).l;
      printf("%.10lf\n", p);
    }
  return 0;
}