Relax! It's Just a Game

Interview

Time limit1sMemory limit128 MB

Summary

For each score (A, B), check whether the binomial coefficient C(A+B, A) equals the sum A+B, and print the comparison.

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

Problem

You: What's the score? Did I miss much?
Me: It's 2-1 for elAhli and the second half just started. The first half was quite boring.
You: Who scored first, elAhli or ezZamalek?
Me: What difference does it make?
You: A big difference! I can predict the outcome of the match if I know the order in which the goals were scored in the first half.
Me: What do you mean?
You: It's 2-1 for elAhli, right? One of three things could have happened: elAhli scored twice and then ezZamalek scored; or elAhli scored, then ezZamalek, then elAhli again; or ezZamalek scored first and then elAhli scored twice.
Me: So?!! I still don't see what difference it makes. It's still 2-1 for elAhli! Why don't you relax and let us watch the game in peace?
You: You don't understand! I believe the probability of who will win depends on the order in which the goals were scored. Now I have to analyze 3 possibilities.
Me: And what if the score were 3-2? What would you do then?
You: I would have to work through 5 different possibilities. Right?
Me: Of course not! The number of possibilities isn't always equal to the sum.
You: Can you tell me when it is equal to the sum?
Me: You're a programmer. Why don't you write a program that counts the number of possibilities and compares it to the sum?
You: I don't have time; I want to watch the match. Besides, I have nine other problems to worry about.
Me: I'll give you a hint. The number of possibilities equals the sum only when one of the teams scored a certain number of goals.

Given a first-half score, the number of possibilities is the number of distinct orders in which the goals could have been scored: if one team scored $A$ goals and the other scored $B$ goals, it equals $\binom{A+B}{A}$ . For each score, decide whether this number of possibilities equals the sum $A+B$ .

Input

The input consists of one or more test cases. Each test case is a single line with two natural numbers $A$ and $B$ (separated by one or more spaces) giving the first-half score. No team scores more than $10$ goals, so $0 \le A, B \le 10$ . Input ends with a line containing two values of $-1$ , which is not part of the test cases.

Output

For each test case, if the number of possibilities equals the sum, print:

A+B=C

where $A$ and $B$ are the two scores and $C$ is their sum. If the number of possibilities is not equal to the sum, replace the = sign with !=.

Examples4

Example 1
Input
```
2 1
1 0
-1 -1
```
Expected output
```
2+1=3
1+0=1
```
Example 2
Input
```
1 1
3 1
1 5
-1 -1
```
Expected output
```
1+1=2
3+1=4
1+5=6
```
Example 3
Input
```
2 2
3 2
0 0
-1 -1
```
Expected output
```
2+2!=4
3+2!=5
0+0!=0
```

Example 4

Input

Expected output

0+1=1
1+0=1
0+2!=2
2+0!=2