Given four integers **A**, **N**, **L** and **R**, the task is to find the **N** th number in a sequence of consecutive integers from **L** to **R** which is not a multiple of **A**. It is given that the sequence contain at least **N** numbers which are not divisible by **A** and the integer **A** is always greater than 1.

**Examples:**

Input:A = 2, N = 3, L = 1, R = 10Output:5Explanation:

The sequence is1, 2,3, 4,5, 6,7, 8,9and 10. Here 5 is the third number which is not a multiple of 2 in the sequence.

Input:A = 3, N = 6, L = 4, R = 20Output:11Explanation :

11 is the 6th number which is not a multiple of 3 in the sequence.

**Naive Approach:** The naive approach is to iterate over the range **[L, R]** in a loop to find the **N ^{th}** number. The steps are:

- Initialize the count of non-multiple number and current number to 0.
- Iterate over the range
**[L, R]**until the count of the non-multiple number is not equal to**N**. - Increment the count of the non-multiple number by 1, If the
**current number is not divisible by A**.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` `// Function to find Nth number not a ` `// multiple of A in the range [L, R] ` `void` `count_no (` `int` `A, ` `int` `N, ` `int` `L, ` `int` `R) ` `{ ` ` ` ` ` `// To store the count ` ` ` `int` `count = 0; ` ` ` `int` `i = 0; ` ` ` `// To check all the nos in range ` ` ` `for` `(i = L; i < R + 1; i++) ` ` ` `{ ` ` ` `if` `(i % A != 0) ` ` ` `count += 1; ` ` ` ` ` `if` `(count == N) ` ` ` `break` `; ` ` ` `} ` ` ` `cout << i; ` `} ` `// Driver code ` `int` `main() ` `{ ` ` ` ` ` `// Given values of A, N, L, R ` ` ` `int` `A = 3, N = 6, L = 4, R = 20; ` ` ` ` ` `// Function Call ` ` ` `count_no (A, N, L, R); ` ` ` `return` `0; ` `} ` `// This code is contributed by mohit kumar 29 ` |

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## Java

`// Java program for the above approach ` `import` `java.util.*;` `import` `java.io.*;` `class` `GFG{` ` ` `// Function to find Nth number not a ` `// multiple of A in the range [L, R] ` `static` `void` `count_no (` `int` `A, ` `int` `N, ` ` ` `int` `L, ` `int` `R)` `{ ` ` ` `// To store the count ` ` ` `int` `count = ` `0` `; ` ` ` `int` `i = ` `0` `; ` ` ` `// To check all the nos in range ` ` ` `for` `(i = L; i < R + ` `1` `; i++) ` ` ` `{ ` ` ` `if` `(i % A != ` `0` `) ` ` ` `count += ` `1` `; ` ` ` ` ` `if` `(count == N) ` ` ` `break` `; ` ` ` `} ` ` ` `System.out.println(i); ` `} ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{` ` ` ` ` `// Given values of A, N, L, R ` ` ` `int` `A = ` `3` `, N = ` `6` `, L = ` `4` `, R = ` `20` `; ` ` ` `// Function call ` ` ` `count_no (A, N, L, R); ` `}` `}` `// This code is contributed by sanjoy_62` |

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## Python3

`# Python3 program for the above approach ` `# Function to find Nth number not a ` `# multiple of A in the range [L, R] ` `def` `count_no (A, N, L, R): ` ` ` `# To store the count ` ` ` `count ` `=` `0` ` ` `# To check all the nos in range ` ` ` `for` `i ` `in` `range` `( L, R ` `+` `1` `): ` ` ` `if` `( i ` `%` `A !` `=` `0` `): ` ` ` `count ` `+` `=` `1` ` ` `if` `( count ` `=` `=` `N ): ` ` ` `break` ` ` `print` `( i ) ` ` ` `# Given values of A, N, L, R ` `A, N, L, R ` `=` `3` `, ` `6` `, ` `4` `, ` `20` `# Function Call ` `count_no (A, N, L, R) ` |

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## C#

`// C# program for the above approach ` `using` `System;` `class` `GFG{` ` ` `// Function to find Nth number not a ` `// multiple of A in the range [L, R] ` `static` `void` `count_no (` `int` `A, ` `int` `N, ` ` ` `int` `L, ` `int` `R)` `{ ` ` ` ` ` `// To store the count ` ` ` `int` `count = 0; ` ` ` `int` `i = 0; ` ` ` `// To check all the nos in range ` ` ` `for` `(i = L; i < R + 1; i++) ` ` ` `{ ` ` ` `if` `(i % A != 0) ` ` ` `count += 1; ` ` ` ` ` `if` `(count == N) ` ` ` `break` `; ` ` ` `} ` ` ` `Console.WriteLine(i); ` `} ` `// Driver code ` `public` `static` `void` `Main() ` `{` ` ` ` ` `// Given values of A, N, L, R ` ` ` `int` `A = 3, N = 6, L = 4, R = 20; ` ` ` `// Function call ` ` ` `count_no (A, N, L, R); ` `}` `}` `// This code is contributed by sanjoy_62` |

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**Output:**

11

**Time Complexity:** *O(R – L)* **Auxiliary Space:** *O(1)*

**Efficient Approach:**

The key observation is that there are **A – 1** numbers that are not divisible by **A** in the range **[1, A – 1]**. Similarly, there are **A – 1** numbers not divisible by **A** in range** [A + 1, 2 * A – 1], [2 * A + 1, 3 * A – 1]** and so on.

With the help of this observation, the **N ^{th}** number which is not divisible by

**A**will be:

To find the value in the range [ **L, R** ], we need to shift the origin from ‘0’ to ‘L – 1’, thus we can say that the N^{th} number which is not divisible by A in the range will be :

However there is an edge case, when the value of **( L – 1 ) + N + floor( ( N – 1 ) / ( A – 1 ) )** itself turns out to be multiple of a **‘A’**, in that case Nth number will be :

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find Nth number` `// not a multiple of A in range [L, R]` `void` `countNo(` `int` `A, ` `int` `N, ` `int` `L, ` `int` `R)` `{` ` ` ` ` `// Calculate the Nth no` ` ` `int` `ans = L - 1 + N + ` `floor` `((N - 1) / ` ` ` `(A - 1));` ` ` ` ` `// Check for the edge case` ` ` `if` `(ans % A == 0)` ` ` `{` ` ` `ans = ans + 1;` ` ` `}` ` ` `cout << ans << endl;` `}` `// Driver Code` `int` `main()` `{` ` ` ` ` `// Input parameters ` ` ` `int` `A = 5, N = 10, L = 4, R = 20;` ` ` ` ` `// Function Call` ` ` `countNo(A, N, L, R);` ` ` ` ` `return` `0;` `}` `// This code is contributed by avanitrachhadiya2155` |

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## Java

`// Java program for the above approach` `import` `java.io.*;` `class` `GFG ` `{` ` ` `// Function to find Nth number` ` ` `// not a multiple of A in range [L, R]` ` ` `static` `void` `countNo(` `int` `A, ` `int` `N, ` `int` `L, ` `int` `R)` ` ` `{` ` ` `// Calculate the Nth no` ` ` `int` `ans = L - ` `1` `+ N + (` `int` `)Math.floor((N - ` `1` `) / (A - ` `1` `));` ` ` `// Check for the edge case` ` ` `if` `(ans % A == ` `0` `)` ` ` `{` ` ` `ans = ans + ` `1` `;` ` ` `}` ` ` `System.out.println(ans); ` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{` ` ` `// Input parameters ` ` ` `int` `A = ` `5` `, N = ` `10` `, L = ` `4` `, R = ` `20` `;` ` ` `// Function Call` ` ` `countNo(A, N, L, R); ` ` ` `}` `}` `// This code is contributed by rag2127` |

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## Python3

`# Python3 program for the above approach` `import` `math` `# Function to find Nth number` `# not a multiple of A in range [L, R]` `def` `countNo (A, N, L, R):` ` ` `# Calculate the Nth no` ` ` `ans ` `=` `L ` `-` `1` `+` `N \` ` ` `+` `math.floor( ( N ` `-` `1` `) ` `/` `( A ` `-` `1` `) )` ` ` ` ` `# Check for the edge case` ` ` `if` `ans ` `%` `A ` `=` `=` `0` `:` ` ` `ans ` `=` `ans ` `+` `1` `;` ` ` `print` `(ans)` `# Input parameters ` `A, N, L, R ` `=` `5` `, ` `10` `, ` `4` `, ` `20` `# Function Call` `countNo(A, N, L, R)` |

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**Output:**

16

**Time Complexity:** *O(1)* **Auxiliary Space:** *O(1)*