# Find if the given number is present in the infinite sequence or not

Given three integers A, B and C. In an infinite sequence, A is the first number, C is the common difference (Si – Si – 1 = C). The task is to check if the number B will appear in the sequence or not.

Examples:

Input: A = 1, B = 7, C = 3
Output: Yes
The sequence will be 1, 4, 7, 10, …

Input: A = 1, B = -4, C = 5
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: There are two cases:

1. When C = 0, print Yes if A = B else No as the sequence will consist only the number A
2. When C > 0, for any non-negative integer k the equation B = A + k * C must be satisfied i.e. (B – A) / C must be a non-negative integer.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if ` `// the sequence will contain B ` `bool` `doesContainB(``int` `a, ``int` `b, ``int` `c) ` `{ ` `    ``if` `(a == b) ` `        ``return` `true``; ` ` `  `    ``if` `((b - a) * c > 0 && (b - a) % c == 0) ` `        ``return` `true``; ` ` `  `    ``return` `false``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 1, b = 7, c = 3; ` ` `  `    ``if` `(doesContainB(a, b, c)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG  ` `{ ` ` `  `    ``// Function that returns true if  ` `    ``// the sequence will contain B  ` `    ``static` `boolean` `doesContainB(``int` `a, ``int` `b, ``int` `c)  ` `    ``{ ` `        ``if` `(a == b)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``if` `((b - a) * c > ``0` `&& (b - a) % c == ``0``)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `a = ``1``, b = ``7``, c = ``3``; ` ` `  `        ``if` `(doesContainB(a, b, c))  ` `        ``{ ` `            ``System.out.println(``"Yes"``); ` `        ``}  ` `        ``else`  `        ``{ ` `            ``System.out.println(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function that returns true if ` `# the sequence will contain B ` `def` `doesContainB(a, b, c): ` `    ``if` `(a ``=``=` `b): ` `        ``return` `True` ` `  `    ``if` `((b ``-` `a) ``*` `c > ``0` `and` `(b ``-` `a) ``%` `c ``=``=` `0``): ` `        ``return` `True` ` `  `    ``return` `False` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``a, b, c ``=` `1``, ``7``, ``3` ` `  `    ``if` `(doesContainB(a, b, c)): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# This code is contributed by 29AjayKumar `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Function that returns true if  ` `    ``// the sequence will contain B  ` `    ``static` `bool` `doesContainB(``int` `a, ``int` `b, ``int` `c)  ` `    ``{ ` `        ``if` `(a == b)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``if` `((b - a) * c > 0 && (b - a) % c == 0)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `a = 1, b = 7, c = 3; ` ` `  `        ``if` `(doesContainB(a, b, c))  ` `        ``{ ` `            ``Console.WriteLine(``"Yes"``); ` `        ``}  ` `        ``else` `        ``{ ` `            ``Console.WriteLine(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

## PHP

 ` 0 &&  ` `        ``(``\$b` `- ``\$a``) % ``\$c` `== 0) ` `        ``return` `true; ` ` `  `    ``return` `false; ` `} ` ` `  `// Driver code ` `\$a` `= 1; ``\$b` `= 7; ``\$c` `= 3; ` ` `  `if` `(doesContainB(``\$a``, ``\$b``, ``\$c``)) ` `    ``echo` `"Yes"``; ` `else` `    ``echo` `"No"``; ` ` `  `// This code is contributed ` `// by Akanksha Rai ` `?> `

Output:

```Yes
```

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