# Check if a number N can be expressed as the sum of powers of X or not

Given two positive numbers **N** and **X**, the task is to check if the given number **N** can be expressed as the sum of distinct powers of **X**. If found to be true, then print **“Yes”**, Otherwise, print **“No”**.

**Examples:**

Input:N = 10, X = 3Output: YesExplanation:The given value of N(= 10) can be written as (1 + 9) = 3^{0}+ 3^{2}. Since all the power of X(= 3) are distinct. Therefore, print Yes.

Input:N= 12, X = 4Output:No

**Approach:** The given problem can be solved by checking if the number **N** can be written in base **X** or not. Follow the steps below to solve the problem:

- Iterate a loop until the value of
**N**is**at least 0**and perform the following steps:- Calculate the value of remainder
**rem**when**N**is divided by**X**. - If the value of
**rem**is**at least 2**, then print**“No”**and return. - Otherwise, update the value of
**N**as**N / X**.

- Calculate the value of remainder
- After completing the above steps, if there doesn’t exist any termination, then print
**“Yes”**as the result at N can be expressed in the distinct power of**X**.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to check if the number N` `// can be expressed as the sum of` `// different powers of X or not` `bool` `ToCheckPowerofX(` `int` `n, ` `int` `x)` `{` ` ` `// While n is a positive number` ` ` `while` `(n > 0) {` ` ` `// Find the remainder` ` ` `int` `rem = n % x;` ` ` `// If rem is at least 2, then` ` ` `// representation is impossible` ` ` `if` `(rem >= 2) {` ` ` `return` `false` `;` ` ` `}` ` ` `// Divide the value of N by x` ` ` `n = n / x;` ` ` `}` ` ` `return` `true` `;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 10, X = 3;` ` ` `if` `(ToCheckPowerofX(N, X)) {` ` ` `cout << ` `"Yes"` `;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"No"` `;` ` ` `}` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG{` `// Function to check if the number N` `// can be expressed as the sum of` `// different powers of X or not` `static` `boolean` `ToCheckPowerofX(` `int` `n, ` `int` `x)` `{` ` ` ` ` `// While n is a positive number` ` ` `while` `(n > ` `0` `)` ` ` `{` ` ` ` ` `// Find the remainder` ` ` `int` `rem = n % x;` ` ` `// If rem is at least 2, then` ` ` `// representation is impossible` ` ` `if` `(rem >= ` `2` `)` ` ` `{` ` ` `return` `false` `;` ` ` `}` ` ` `// Divide the value of N by x` ` ` `n = n / x;` ` ` `}` ` ` `return` `true` `;` `}` `// Driver Code` `public` `static` `void` `main (String[] args)` `{` ` ` `int` `N = ` `10` `, X = ` `3` `;` ` ` `if` `(ToCheckPowerofX(N, X))` ` ` `{` ` ` `System.out.print(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `System.out.print(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by sanjoy_62` |

## Python3

`# Python3 program for the above approach` `# Function to check if the number N` `# can be expressed as the sum of` `# different powers of X or not` `def` `ToCheckPowerofX(n, x):` ` ` ` ` `# While n is a positive number` ` ` `while` `(n > ` `0` `):` ` ` ` ` `# Find the remainder` ` ` `rem ` `=` `n ` `%` `x` ` ` `# If rem is at least 2, then` ` ` `# representation is impossible` ` ` `if` `(rem >` `=` `2` `):` ` ` `return` `False` ` ` `# Divide the value of N by x` ` ` `n ` `=` `n ` `/` `/` `x` ` ` `return` `True` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `N ` `=` `10` ` ` `X ` `=` `3` ` ` ` ` `if` `(ToCheckPowerofX(N, X)):` ` ` `print` `(` `"Yes"` `)` ` ` `else` `:` ` ` `print` `(` `"No"` `)` ` ` `# This code is contributed by bgangwar59` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` ` ` `// Function to check if the number N` `// can be expressed as the sum of` `// different powers of X or not` `static` `bool` `ToCheckPowerofX(` `int` `n, ` `int` `x)` `{` ` ` ` ` `// While n is a positive number` ` ` `while` `(n > 0)` ` ` `{` ` ` ` ` `// Find the remainder` ` ` `int` `rem = n % x;` ` ` `// If rem is at least 2, then` ` ` `// representation is impossible` ` ` `if` `(rem >= 2)` ` ` `{` ` ` `return` `false` `;` ` ` `}` ` ` `// Divide the value of N by x` ` ` `n = n / x;` ` ` `}` ` ` `return` `true` `;` `}` `// Driver code` `public` `static` `void` `Main(String []args)` `{` ` ` `int` `N = 10, X = 3;` ` ` `if` `(ToCheckPowerofX(N, X))` ` ` `{` ` ` `Console.Write(` `"Yes"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `Console.Write(` `"No"` `);` ` ` `}` `}` `}` `// This code is contributed by code_hunt,` |

## Javascript

`<script>` `// JavaScripts program for the above approach` `// Function to check if the number N` `// can be expressed as the sum of` `// different powers of X or not` `function` `ToCheckPowerofX(n, x)` `{` ` ` `// While n is a positive number` ` ` `while` `(n > 0) {` ` ` `// Find the remainder` ` ` `var` `rem = n % x;` ` ` `// If rem is at least 2, then` ` ` `// representation is impossible` ` ` `if` `(rem >= 2) {` ` ` `return` `false` `;` ` ` `}` ` ` `// Divide the value of N by x` ` ` `n = n / x;` ` ` `}` ` ` `return` `true` `;` `}` `// Driver Code` ` ` `var` `N = 10, X = 3;` ` ` `if` `(ToCheckPowerofX(N, X)) {` ` ` `document.write(` `"Yes"` `);` ` ` `}` ` ` `else` `{` ` ` `document.write(` `"No"` `);` ` ` `}` `</script>` |

**Output:**

Yes

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