Cheeseburger Making 2

Interview

Time limit1sMemory limit1024 MB

Summary

Given A patties and B cheese slices, decide whether every item can go into burgers that each have exactly one more patty than cheese, and print one valid build if so.

Level: Easy3 of 10
Topics: Implementation, Math
Solved: No attempts yet

Problem

Seunghyun works at a burger shop that has $A$ hamburger patties and $B$ slices of cheese to use as ingredients. To make a cheeseburger, pick at least one patty and at least one slice of cheese, then stack the patties and cheese alternately between the bun halves. The number of patties chosen must be exactly one more than the number of cheese slices.

Seunghyun wants to make some cheeseburgers and use up every ingredient in the shop. Find how each cheeseburger should be made so that all patties and cheese slices are used.

Input

The first line contains two integers $A(2\leq A\leq 100)$ and $B(1\leq B\leq 100)$ , separated by a space. $A$ is the number of patties and $B$ is the number of cheese slices.

Output

On the first line, print YES if there is a way to use every patty and every cheese slice, otherwise print NO.

If such a way exists, print the number of cheeseburgers $K$ on the second line. Then, from the third line on, print $K$ lines, each a string $S$ that describes how to build one cheeseburger. If the $i$ -th ingredient is a patty, the $i$ -th character is a. If it is cheese, the $i$ -th character is b.

If there are several valid answers, print any one of them.

Examples4

Example 1
Input
```
8 5
```
Expected output
```
YES
3
aba
ababa
ababa
```
Example 2
Input
```
3 4
```
Expected output
```
NO
```
Example 3
Input
```
4 2
```
Expected output
```
YES
2
aba
aba
```
Example 4
Input
```
8 3
```
Expected output
```
NO
```