Hi guys,here I'd like to share my problem set in an interesting way. All the problems are created by myself.

They contain my aesthetic of problems: the neater,the better. It should be also interesting and best to have educational significance.

You can find the editorial for all the problems in the link,so I will only write down some interesting points under the statement.

Let's go :)

1.Increasing and Decreasing

Construct an array $$$a$$$ consisting of $$$n$$$ integers which satisfies the following conditions:

• $$$a_1=x,a_n=y$$$;
• $$$a$$$ is strictly increasing;
• if we denote $$$b_i=a_{i+1}-a_{i}$$$ for $$$1 \leq i \leq n-1$$$, then $$$b$$$ is strictly decreasing.

2.(Yet Another) Increasing and Decreasing

Construct an array $$$a$$$ consisting of $$$n$$$ integers which satisfies the following conditions:

• $$$a_1=x$$$;
• $$$a_n<2^30$$$
• $$$a$$$ is strictly increasing;
• if we denote $$$b_i=a_{i+1}⊕a_{i}$$$ for $$$1 \leq i \leq n-1$$$, then $$$b$$$ is strictly decreasing($$$⊕$$$ is bitwise-xor).