# Largest number less than or equal to Z that leaves a remainder X when divided by Y

Given three integers x, y, z, the task is to find the largest non-negative number less than or equal to z that leaves a remainder x when divided by y (Given x < y). If no such number exists then the output will be -1.

Examples:

```Input: x = 1, y = 5, z = 8
Output: 6
Explanation:
6 is the largest number less than 8
which when divided by 5
leaves a remainder 1.

Input: x = 4, y = 6, z = 3
Output: -1
Explanation:
Since no such number exists the output is -1
```

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

Approach: To solve the problem mentioned above the very first observation is if x > z then answer will not be possible, so output will be -1.

Let the required number be p. Following are the two equations for solving the problem:

• p * y + x = 0
• p * y <= (z – x)

In order to find the answer, we need to find the value of p. So,

`p = (z - x) / y`

After calculating p we can simply find the answer which is

`p * y + x`

Below is the implementation of the above approach:

## C++

 `// C++ implementation to Find the ` `// largest non-negative number that ` `// is less than or equal to integer Z ` `// and leaves a remainder X when divided by Y ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to get the number ` `int` `get(``int` `x, ``int` `y, ``int` `z) ` `{ ` ` `  `    ``// remainder can't be larger ` `    ``// than the largest number, ` `    ``// if so then answer doesn't exist. ` `    ``if` `(x > z) ` `        ``return` `-1; ` ` `  `    ``// reduce number by x ` `    ``int` `val = z - x; ` ` `  `    ``// finding the possible ` `    ``// number that is divisible by y ` `    ``int` `div` `= (z - x) / y; ` ` `  `    ``// this number is always <= x ` `    ``// as we calculated over z - x ` `    ``int` `ans = ``div` `* y + x; ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// initialise the three integers ` `    ``int` `x = 1, y = 5, z = 8; ` ` `  `    ``cout << get(x, y, z) << ``"\n"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to Find the ` `// largest non-negative number that ` `// is less than or equal to integer Z ` `// and leaves a remainder X when divided by Y ` `class` `GFG{ ` `  `  `// Function to get the number ` `static` `int` `get(``int` `x, ``int` `y, ``int` `z) ` `{ ` `  `  `    ``// remainder can't be larger ` `    ``// than the largest number, ` `    ``// if so then answer doesn't exist. ` `    ``if` `(x > z) ` `        ``return` `-``1``; ` `  `  `    ``// reduce number by x ` `    ``int` `val = z - x; ` `  `  `    ``// finding the possible ` `    ``// number that is divisible by y ` `    ``int` `div = (z - x) / y; ` `  `  `    ``// this number is always <= x ` `    ``// as we calculated over z - x ` `    ``int` `ans = div * y + x; ` `  `  `    ``return` `ans; ` `} ` `  `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``// initialise the three integers ` `    ``int` `x = ``1``, y = ``5``, z = ``8``; ` `  `  `    ``System.out.print(get(x, y, z)+ ``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

## Python3

 `# Python implementation to Find the ` `# largest non-negative number that ` `# is less than or equal to integer Z ` `# and leaves a remainder X when divided by Y ` ` `  `# Function to get the number ` `def` `get(x, y, z): ` `     `  `    ``# remainder can't be larger ` `    ``# than the largest number, ` `    ``# if so then answer doesn't exist. ` `    ``if` `(x > z): ` `        ``return` `-``1` `         `  `    ``# reduce number by x ` `    ``val ``=` `z ``-` `x ` `     `  `    ``# finding the possible ` `    ``# number that is divisible by y ` `    ``div ``=` `(z ``-` `x) ``/``/` `y ` `     `  `     `  `    ``# this number is always <= x ` `    ``# as we calculated over z - x ` `    ``ans ``=` `div ``*` `y ``+` `x ` `     `  `    ``return` `ans ` ` `  ` `  `# Driver Code ` `# initialise the three integers ` `x ``=` `1` `y ``=` `5` `z ``=` `8` ` `  `print``(get(x, y, z)) ` ` `  `# This code is contributed by shubhamsingh10 `

## C#

 `// C# implementation to Find the ` `// largest non-negative number that ` `// is less than or equal to integer Z ` `// and leaves a remainder X when divided by Y ` `using` `System; ` ` `  `class` `GFG{ ` `   `  `// Function to get the number ` `static` `int` `get``(``int` `x, ``int` `y, ``int` `z) ` `{ ` `   `  `    ``// remainder can't be larger ` `    ``// than the largest number, ` `    ``// if so then answer doesn't exist. ` `    ``if` `(x > z) ` `        ``return` `-1; ` `   `  `    ``// reduce number by x ` `    ``int` `val = z - x; ` `   `  `    ``// finding the possible ` `    ``// number that is divisible by y ` `    ``int` `div = (z - x) / y; ` `   `  `    ``// this number is always <= x ` `    ``// as we calculated over z - x ` `    ``int` `ans = div * y + x; ` `   `  `    ``return` `ans; ` `} ` `   `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``// initialise the three integers ` `    ``int` `x = 1, y = 5, z = 8; ` `   `  `    ``Console.Write(``get``(x, y, z)+ ``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

Output:

```6
```

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