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 = (int)1e5 + 7;
struct SegmentType {
  int l, r;
  double a, b;
};
int n, q, a[MaxN], b[MaxN];
bool flg;
SegmentType ans, seg[MaxN << 2];
void MakeSeg(int x, int l, int r) {
  seg[x].l = l;
  seg[x].r = r;
  if (l == r) {
    seg[x].a = 1.0 * a[l] / b[l];
    seg[x].b = 1.0 - 1.0 * a[l] / b[l];
    return;
  }
  int lc = x << 1, mi = (l + r) >> 1;
  MakeSeg(lc, l, mi);
  MakeSeg(lc + 1, mi + 1, r);
  double t1 = (1 - seg[lc + 1].a) * (1 - seg[lc].b);
  double t2 = (1 - seg[lc].b) * (1 - seg[lc + 1].a);
  seg[x].a = seg[lc].a * seg[lc + 1].a / (1 - t1);
  seg[x].b = seg[lc + 1].b * seg[lc].b / (1 - t2);
}
void Update(int x, int id, int a, int b) {
  if (seg[x].l == seg[x].r) {
    seg[x].a = 1.0 * a / b;
    seg[x].b = 1.0 - 1.0 * a / b;
    return;
  }
  int lc = x << 1;
  if (id <= seg[x << 1].r)
    Update(x << 1, id, a, b);
  else
    Update((x << 1) + 1, id, a, b);
  double t1 = (1 - seg[lc + 1].a) * (1 - seg[lc].b);
  double t2 = (1 - seg[lc].b) * (1 - seg[lc + 1].a);
  seg[x].a = seg[lc].a * seg[lc + 1].a / (1 - t1);
  seg[x].b = seg[lc + 1].b * seg[lc].b / (1 - t2);
}
void Calc(int x, int l, int r) {
  if (l <= seg[x].l && seg[x].r <= r) {
    if (flg) {
      ans.a = seg[x].a;
      ans.b = seg[x].b;
      flg = false;
      return;
    }
    double t1, t2;
    t1 = (1 - seg[x].a) * (1 - ans.b);
    t2 = (1 - ans.b) * (1 - seg[x].a);
    ans.a = ans.a * seg[x].a / (1 - t1);
    ans.b = ans.b * seg[x].b / (1 - t2);
    return;
  }
  int lc = x << 1;
  if (l <= seg[lc].r) Calc(lc, l, r);
  if (seg[lc].r < r) Calc(lc + 1, l, r);
}
int main() {
  int i, typ, id, l, r;
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d%d", a + i, b + i);
  MakeSeg(1, 1, n);
  for (i = 1; i <= q; i++) {
    scanf("%d", &typ);
    if (typ == 1) {
      scanf("%d%d%d", &id, &l, &r);
      Update(1, id, l, r);
    } else {
      scanf("%d%d", &l, &r);
      flg = true;
      Calc(1, l, r);
      printf("%lf\n", ans.a);
    }
  }
  return 0;
}