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>
const int N = 1e5 + 10;
int n, q;
struct mat {
  long double a[2][2];
  mat() : a() {}
  inline mat operator*(const mat &x) const {
    mat ans;
    ans.a[0][0] = a[0][0] * x.a[0][0] + a[0][1] * x.a[1][0];
    ans.a[0][1] = a[0][0] * x.a[0][1] + a[0][1] * x.a[1][1];
    ans.a[1][0] = a[1][0] * x.a[0][0] + a[1][1] * x.a[1][0];
    ans.a[1][1] = a[1][0] * x.a[0][1] + a[1][1] * x.a[1][1];
    return ans;
  }
} sum[N << 2], f;
void update(int rt, int l, int r, int p) {
  if (l == r) {
    int x, y;
    scanf("%d%d", &x, &y);
    sum[rt].a[0][0] = (long double)y / x;
    sum[rt].a[1][0] = (long double)(x - y) / x;
    sum[rt].a[0][1] = 1;
    return;
  }
  int m = (l + r) >> 1;
  p <= m ? update(rt << 1, l, m, p) : update(rt << 1 | 1, m + 1, r, p);
  sum[rt] = sum[rt << 1] * sum[rt << 1 | 1];
}
mat query(int rt, int l, int r, int ql, int qr) {
  if (ql == l && r == qr) return sum[rt];
  int m = (l + r) >> 1;
  if (qr <= m)
    return query(rt << 1, l, m, ql, qr);
  else if (ql > m)
    return query(rt << 1 | 1, m + 1, r, ql, qr);
  else
    return query(rt << 1, l, m, ql, m) *
           query(rt << 1 | 1, m + 1, r, m + 1, qr);
}
int main() {
  double mn = (long double)1 / (long double)-1e-1000,
         mx = (long double)1 / (long double)1e-1000, ans;
  int i, op, x, y;
  scanf("%d%d", &n, &q);
  f.a[0][0] = 1;
  for (i = 1; i <= n; i++) update(1, 1, n, i);
  while (q--) {
    scanf("%d", &op);
    if (op == 1)
      scanf("%d", &i), update(1, 1, n, i);
    else
      scanf("%d%d", &x, &y),
          ans = 1 / (f * query(1, 1, n, x, y)).a[0][0],
          printf("%.10lf\n", (ans > mn && ans < mx) ? ans : 0);
  }
  return 0;
}