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 + 10;
struct edge {
  int l, r;
  double a, b;
} tr[maxn << 2];
int n, q;
double ans1, ans2;
double p[maxn];
void pushup(int rt) {
  tr[rt].a = tr[rt << 1].a * tr[rt << 1 | 1].a;
  tr[rt].b = tr[rt << 1].b + tr[rt << 1].a * tr[rt << 1 | 1].b;
}
void build(int l, int r, int rt) {
  tr[rt].l = l, tr[rt].r = r;
  if (l == r) {
    tr[rt].a = tr[rt].b = (1 - p[l]) / p[l];
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  pushup(rt);
}
void update(int pos, int rt, double val) {
  int l = tr[rt].l, r = tr[rt].r;
  if (l == r) {
    tr[rt].a = tr[rt].b = (1 - val) / val;
    return;
  }
  int mid = (l + r) >> 1;
  if (pos <= mid)
    update(pos, rt << 1, val);
  else
    update(pos, rt << 1 | 1, val);
  pushup(rt);
  return;
}
void query(int L, int R, int rt) {
  int l = tr[rt].l, r = tr[rt].r;
  if (L <= l & r <= R) {
    ans2 += ans1 * tr[rt].b;
    ans1 *= tr[rt].a;
    return;
  }
  int mid = (l + r) >> 1;
  if (L <= mid) query(L, R, rt << 1);
  if (R > mid) query(L, R, rt << 1 | 1);
}
int x, y, z, op;
int main() {
  scanf("%d%d", &n, &q);
  for (int i = 1; i <= n; i++) scanf("%d%d", &x, &y), p[i] = x * 1.0 / y;
  build(1, n, 1);
  while (q--) {
    scanf("%d", &op);
    if (op == 1) {
      scanf("%d%d%d", &x, &y, &z);
      update(x, 1, y * 1.0 / z);
    } else {
      scanf("%d%d", &x, &y);
      ans1 = 1;
      ans2 = 0;
      query(x, y, 1);
      if (ans2 <= 1e15)
        ans1 = 1 / (1 + ans2);
      else
        ans1 = 0;
      printf("%.10lf\n", ans1);
    }
  }
  return 0;
}