301206: CF225E. Unsolvable
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
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Description
Unsolvable
题意翻译
求所有使方程 $$ z = \lfloor \frac{x}{2} \rfloor + y + xy $$ 不存在正整数解 $\left( x, y\right)$ 的 $z$ 中,第 $n$ 小的 $z$ ,结果对 $10^9 + 7$ 取模题目描述
Consider the following equation: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF225E/546df2c440088cc1d07628a3b2e6a0b61a00f3dc.png) where sign $ [a] $ represents the integer part of number $ a $ .Let's find all integer $ z $ $ (z>0) $ , for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers $ x $ and $ y $ $ (x,y>0) $ , for which the given above equation holds. Let's write out all such $ z $ in the increasing order: $ z_{1},z_{2},z_{3} $ , and so on $ (z_{i}<z_{i+1}) $ . Your task is: given the number $ n $ , find the number $ z_{n} $ .输入输出格式
输入格式
The first line contains a single integer $ n $ ( $ 1<=n<=40 $ ).
输出格式
Print a single integer — the number $ z_{n} $ modulo $ 1000000007 $ $ (10^{9}+7) $ . It is guaranteed that the answer exists.
输入输出样例
输入样例 #1
1
输出样例 #1
1
输入样例 #2
2
输出样例 #2
3
输入样例 #3
3
输出样例 #3
15