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;
double prob[100010];
struct segmentS {
  int l;
  int r;
  double L;
  double R;
  segmentS *sl, *sr;
};
segmentS* createSegment(int l, int r) {
  segmentS* toRet = new segmentS();
  toRet->l = l;
  toRet->r = r;
  if (l == r) {
    toRet->L = toRet->R = prob[l];
    return toRet;
  }
  int mid = (l + r) / 2;
  toRet->sl = createSegment(l, mid);
  toRet->sr = createSegment(mid + 1, r);
  double l1, l2, r1, r2;
  l1 = toRet->sl->L;
  l2 = toRet->sr->L;
  r1 = toRet->sl->R;
  r2 = toRet->sr->R;
  toRet->L = l1 * l2 / (1 - (1 - l2) * r1);
  toRet->R = r2 + ((1 - r2) * l2 * r1 / (1 - (r1 * (1 - l2))));
  return toRet;
}
pair<double, double> query(segmentS* s, int l, int r) {
  if (s->l > r || s->r < l) return pair<double, double>(1, 1);
  if (l <= s->l && s->r <= r) {
    return pair<double, double>(s->L, s->R);
  } else if (s->sl->r < l) {
    return query(s->sr, l, r);
  } else if (s->sr->l > r) {
    return query(s->sl, l, r);
  } else {
    pair<double, double> left = query(s->sl, l, r);
    pair<double, double> right = query(s->sr, l, r);
    pair<double, double> toRet;
    double l1, l2, r1, r2;
    l1 = left.first;
    l2 = right.first;
    r1 = left.second;
    r2 = right.second;
    toRet.first = l1 * l2 / (1 - (1 - l2) * r1);
    toRet.second = r2 + ((1 - r2) * l2 * r1 / (1 - (r1 * (1 - l2))));
    return toRet;
  }
}
void update(segmentS* s, int x) {
  if (s->l == x && s->r == x) {
    s->L = s->R = prob[x];
    return;
  } else {
    if (s->sl->r < x) {
      update(s->sr, x);
    } else {
      update(s->sl, x);
    }
    double l1, l2, r1, r2;
    l1 = s->sl->L;
    l2 = s->sr->L;
    r1 = s->sl->R;
    r2 = s->sr->R;
    s->L = l1 * l2 / (1 - (1 - l2) * r1);
    s->R = r2 + ((1 - r2) * l2 * r1 / (1 - (r1 * (1 - l2))));
  }
}
int main() {
  int n, q;
  scanf("%d %d", &n, &q);
  for (int i = 0; i < n; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    prob[i] = double(a) / b;
  }
  segmentS* segmentRoot = createSegment(0, n - 1);
  for (int i = 0; i < q; i++) {
    int a;
    scanf("%d", &a);
    if (a == 2) {
      int x, y;
      scanf("%d %d", &x, &y);
      x--;
      y--;
      printf("%.10lf\n", query(segmentRoot, x, y).first);
    } else {
      int i, x, y;
      scanf("%d %d %d", &i, &x, &y);
      i--;
      prob[i] = double(x) / y;
      update(segmentRoot, i);
    }
  }
}