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;
template <class _T>
inline void rd(_T &_a) {
  int _f = 0, _ch = getchar();
  _a = 0;
  while (_ch < '0' || _ch > '9') {
    if (_ch == '-') _f = 1;
    _ch = getchar();
  }
  while (_ch >= '0' && _ch <= '9') _a = _a * 10 + _ch - '0', _ch = getchar();
  if (_f) _a = -_a;
}
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
const int N = 1e5 + 5;
struct ssr {
  double a, b;
} X;
struct tree {
  ssr s;
} t[N << 2];
int P, L, R, n, F;
double p[N];
ssr mg(ssr s1, ssr s2) { return (ssr){s1.a * s2.a, s1.b + s1.a * s2.b}; }
void Pu(int rt) { t[rt].s = mg(t[rt << 1].s, t[rt << 1 | 1].s); }
void Ch(int rt, double x) { t[rt].s.a = t[rt].s.b = 1 / x - 1; }
void Bd(int l, int r, int rt = 1) {
  if (l == r) return Ch(rt, p[l]);
  int m = l + r >> 1;
  Bd(l, m, rt << 1);
  Bd(m + 1, r, rt << 1 | 1);
  Pu(rt);
}
void Ud(int l, int r, int rt = 1) {
  if (l == r) return Ch(rt, p[l]);
  int m = l + r >> 1;
  if (P > m)
    Ud(m + 1, r, rt << 1 | 1);
  else
    Ud(l, m, rt << 1);
  Pu(rt);
}
void Qy(int l, int r, int rt = 1) {
  if (l >= L && r <= R) {
    X = mg(X, t[rt].s);
    return;
  }
  int m = l + r >> 1;
  if (L <= m) Qy(l, m, rt << 1);
  if (R > m) Qy(m + 1, r, rt << 1 | 1);
}
void pud(int u) {
  P = u;
  Ud(1, n);
}
void pqy(int l, int r) {
  X = (ssr){1, 0};
  L = l;
  R = r;
  Qy(1, n);
}
int main() {
  int m;
  rd(n);
  rd(m);
  for (int i = 1, x, y; i <= n; i++) rd(x), rd(y), p[i] = (double)x / y;
  Bd(1, n);
  for (int op, u, x, y; m; m--) {
    rd(op);
    rd(u);
    rd(x);
    if (op == 1)
      rd(y), p[u] = (double)x / y, pud(u);
    else
      pqy(u, x), printf("%.10f\n", X.b != X.b ? 0 : 1 / (1 + X.b)), F++;
  }
  return 0;
}