There are n casinos lined in a row. If Memory plays at casino i , he has probability p i to win and move to the casino on the right ( i + 1 ) or exit the row (if i = n ), and a probability 1 - p i 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 . 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. p i ≤ p i + 1 for all i from 1 to n - 1 . Please help Memory by answering all his requests! 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 a i and b i ( 1 ≤ a i < b i ≤ 10 9 ) — is the probability p i of winning in casino i . The next q lines each contain queries of one of the types specified above ( 1 ≤ a < b ≤ 10 9 , 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. 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