Description

Reimu is given 3 real numbers $n$, $a$, $b$ ($4 \le n \le 5$, $5 \le a,b \le 10$). She successfully computed $n^a+n^b$, and got a result that shows only the integer part on the calculator.

Reimu wants to know: if there exists a real number $n'(n' \geq 0)$ such that the result of ${n'}^a+{n'}^b$ shown on the calculator is exactly the same as the result shown for $n^a+n^b$, then what is the range of possible values of $n'$, i.e., the difference between the maximum and minimum possible $n'$.

If you do not know how to compute $n^k$, please use the pow() function in the cmath library. The result of pow(n,k) is $n^k$.

To increase the difficulty of this problem, Reimu gives you $T$ queries. To reduce your input and output to some extent, we generate the queries using the following code (the code comes from Kawashiro Heavy Industries):

namespace Mker
{
//  Powered By Kawashiro_Nitori
//  Made In Gensokyo, Nihon
	#define uint unsigned int
	uint sd;int op;
	inline void init() {scanf("%u %d", &sd, &op);}
	inline uint uint_rand()
	{
		sd ^= sd << 13;
		sd ^= sd >> 7;
		sd ^= sd << 11;
		return sd;
	}
	inline double get_n()
	{
		double x = (double) (uint_rand() % 100000) / 100000;
		return x + 4;
	}
	inline double get_k()
	{
		double x = (double) (uint_rand() % 100000) / 100000;
		return (x + 1) * 5;
	}
	inline void read(double &n,double &a, double &b)
	{
		n = get_n(); a = get_k();
		if (op) b = a;
		else b = get_k(); 
	}
}

After calling Mker::init(), when you call Mker::read(n,a,b) for the $i$-th time, you will obtain the $i$-th query’s $n_i$, $a_i$, and $b_i$.

To reduce your output, let the answer to the $i$-th query be $s_i$. You only need to output $\sum^{T}_{i=1} s_i$. If the absolute error between your answer and the standard answer is within $10^{-2}$, your answer will be considered correct.

The testdata of this problem is generated using a high (da) precision (bao) algorithm with a time complexity much worse than normal algorithms, to ensure accuracy. The testdata guarantees that the error of each single query is less than $10^{-10}$, so the SPJ tolerance for this problem is completely sufficient for correct solutions.

To help you solve the problem, here is an explanation of $op$:

• When $op=1$, we have $a=b$. Otherwise, there is no special constraint.

Input Format

The input contains one line with $3$ positive integers $T$, $seed$, $op$. Their meanings are described in the problem statement.

Output Format

Output one line, the answer required in the problem statement.

500 233 0

0.00503

10000 3141592653 0

0.10166

50000 1314159 0

0.50722

50000 1314159 1

1.51676

1000000 5201314 0

10.30487

Hint

Subtasks

Source

Lost House 2019 League (MtOI2019) T2

Problem setter: disangan233

Problem reviewer: suwakow

Translated by ChatGPT 5