# Find numbers a and b that satisfy the given conditions

Given an integer n, the task is to find two integers a and b which satisfy the below conditions:

1. a % b = 0
2. a * b > n
3. a / b < n

If no pair satisfies the above conditions then print -1.
Note: There can be multiple (a, b) pairs satisfying the above conditions for n.

Examples:

```Input: n = 10
Output: a = 90, b = 10
90 % 10 = 0
90 * 10 = 900 > 10
90 / 10 = 9 < 10
All three conditions are satisfied.

Input: n = 1
Output: -1
```

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

Approach: Let’s suppose b = n, by taking this assumption a can be found based on the given conditions:

• (a % b = 0) => a should be multiple of b.
• (a / b < n) => a / b = n – 1 which is < n.
• (a * b > n) => a = n.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to print the required numbers ` `void` `find(``int` `n) ` `{ ` `    ``// Suppose b = n and we want a % b = 0 and also ` `    ``// (a / b) < n so a = b * (n - 1) ` `    ``int` `b = n; ` `    ``int` `a = b * (n - 1); ` ` `  `    ``// Special case if n = 1 ` `    ``// we get a = 0 so (a * b) < n ` `    ``if` `(a * b > n && a / b < n) { ` `        ``cout << ``"a = "` `<< a << ``", b = "` `<< b; ` `    ``} ` ` `  `    ``// If no pair satisfies the conditions ` `    ``else` `        ``cout << -1 << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``find(n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach  ` ` `  `public` `class` `GFG{ ` ` `  `    ``// Function to print the required numbers  ` `    ``static` `void` `find(``int` `n)  ` `    ``{  ` `        ``// Suppose b = n and we want a % b = 0 and also  ` `        ``// (a / b) < n so a = b * (n - 1)  ` `        ``int` `b = n;  ` `        ``int` `a = b * (n - ``1``);  ` `     `  `        ``// Special case if n = 1  ` `        ``// we get a = 0 so (a * b) < n  ` `        ``if` `(a * b > n && a / b < n) {  ` `            ``System.out.print(``"a = "` `+ a + ``", b = "` `+ b);  ` `        ``}  ` `     `  `        ``// If no pair satisfies the conditions  ` `        ``else` `            ``System.out.println(-``1``);  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String []args) ` `    ``{  ` `        ``int` `n = ``10``;  ` `        ``find(n);  ` `    ``}  ` `    ``// This code is contributed by Ryuga ` `} `

## Python3

 `# Python3 implementation of the above approach  ` ` `  `# Function to print the required numbers  ` `def` `find(n):  ` ` `  `    ``# Suppose b = n and we want a % b = 0  ` `    ``# and also (a / b) < n so a = b * (n - 1)  ` `    ``b ``=` `n  ` `    ``a ``=` `b ``*` `(n ``-` `1``)  ` ` `  `    ``# Special case if n = 1  ` `    ``# we get a = 0 so (a * b) < n  ` `    ``if` `a ``*` `b > n ``and` `a ``/``/` `b < n:  ` `        ``print``(``"a = {}, b = {}"` `. ``format``(a, b))  ` `     `  `    ``# If no pair satisfies the conditions  ` `    ``else``: ` `        ``print``(``-``1``)  ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``:  ` ` `  `    ``n ``=` `10` `    ``find(n)  ` ` `  `# This code is contributed by Rituraj Jain `

## C#

 `// C# implementation of the above approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to print the required numbers  ` `static` `void` `find(``int` `n)  ` `{  ` `    ``// Suppose b = n and we want a % b = 0  ` `    ``// and also (a / b) < n so a = b * (n - 1)  ` `    ``int` `b = n;  ` `    ``int` `a = b * (n - 1);  ` ` `  `    ``// Special case if n = 1  ` `    ``// we get a = 0 so (a * b) < n  ` `    ``if` `(a * b > n && a / b < n)  ` `    ``{  ` `        ``Console.Write(``"a = "` `+ a + ``", b = "` `+ b);  ` `    ``}  ` ` `  `    ``// If no pair satisfies the conditions  ` `    ``else` `        ``Console.WriteLine(-1);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main() ` `{  ` `    ``int` `n = 10;  ` `    ``find(n);  ` `}  ` `} ` ` `  `// This code is contributed  ` `// by Akanksha Rai `

## PHP

 ` ``\$n` `&& ``\$a` `/ ``\$b` `<``\$n``) { ` `        ``echo` `"a = "` `, ``\$a` `, ``", b = "` `, ``\$b``; ` `    ``} ` ` `  `    ``// If no pair satisfies the conditions ` `    ``else` `        ``echo` `-1 ; ` `} ` ` `  `// Driver code ` ` `  `    ``\$n` `= 10; ` `    ``find(``\$n``); ` `// This code is contributed  ` `// by inder_verma.. ` `?> `

Output:

```a = 90, b = 10
```

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