H. SYSU III
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

As you all know, you are participating in the SYSUCPC (SYSU Constructive Problem Contest) finals. Undoubtedly, the Constructive Kingdom of Sun Yat-sen University is eager for you to tackle some related problems.

Given a string $$$S$$$ containing only lowercase letters, determine the maximum number of disjoint subsequences of length $$$4$$$ that can be formed, such that all subsequences are sysu. Formally, a subsequence of a string $$$S$$$ is a subset of characters of $$$S$$$ that read from left to right.

A greedy algorithm is currently used: each time, starting from the end, an unused u is considered, and it is matched with nearest unused s,y,s sequentially to form a qualified subsequence, which is then removed.

You are now requested to provide a string $$$S$$$ such that the answer obtained by the greedy method is $$$x$$$, while the correct answer is $$$y$$$. If no such $$$S$$$ exists, output $$$-1$$$.

Input

The only line contains two integers $$$x,y(1\leq x,y\leq 10^5)$$$.

Output

A string $$$S$$$ such that the answer obtained by the greedy method is $$$x$$$, while the correct answer is $$$y$$$. If no such $$$S$$$ exists, output $$$-1$$$. The length of $$$S$$$ must not exceed $$$4\times 10^5$$$.

Examples
Input
1 1
Output
ilovesysu
Input
2 1
Output
-1