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 = 110000, mod = 1e9 + 7;
int x[N], y[N];
struct data {
  long double a, b, c, d;
  data() {}
  data(long double a, long double b, long double c, long double d)
      : a(a), b(b), c(c), d(d) {}
} t[N << 2];
data add(data x, data y) {
  data z;
  long double t = 1.0 - y.a * x.d;
  z.a = x.a + x.b * x.c * y.a / t;
  z.b = x.b * y.b / t;
  z.c = x.c * y.c / t;
  z.d = y.d + x.d * y.b * y.c / t;
  return z;
}
void build(int rt, int l, int r) {
  if (l == r) {
    t[rt].b = t[rt].d = 1.0 * x[l] / y[l];
    t[rt].a = t[rt].c = 1 - t[rt].b;
    return;
  }
  int m = l + r >> 1;
  build(rt << 1, l, m);
  build(rt << 1 | 1, m + 1, r);
  t[rt] = add(t[rt << 1], t[rt << 1 | 1]);
}
void updata(int rt, int l, int r, int z) {
  if (l == r) {
    t[rt].b = t[rt].d = 1.0 * x[l] / y[l];
    t[rt].a = t[rt].c = 1 - t[rt].b;
    return;
  }
  int m = l + r >> 1;
  if (z <= m)
    updata(rt << 1, l, m, z);
  else
    updata(rt << 1 | 1, m + 1, r, z);
  t[rt] = add(t[rt << 1], t[rt << 1 | 1]);
}
data query(int rt, int l, int r, int tl, int tr) {
  if (tl <= l && r <= tr) return t[rt];
  int m = l + r >> 1;
  if (tr <= m)
    return query(rt << 1, l, m, tl, tr);
  else if (m < tl)
    return query(rt << 1 | 1, m + 1, r, tl, tr);
  else
    return add(query(rt << 1, l, m, tl, m),
               query(rt << 1 | 1, m + 1, r, m + 1, tr));
}
int main() {
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) scanf("%d%d", &x[i], &y[i]);
  build(1, 1, n);
  while (q--) {
    int t, u, v, w;
    scanf("%d%d%d", &t, &u, &v);
    if (t == 2) {
      data tmp = query(1, 1, n, u, v);
      printf("%.10f\n", (double)tmp.b);
    } else {
      scanf("%d", &w);
      x[u] = v;
      y[u] = w;
      updata(1, 1, n, u);
    }
  }
}