# Check whether a number can be represented as sum of K distinct positive integers

Given two integers **N** and **K**, the task is to check whether **N** can be represented as sum of **K** distinct positive integers.

**Examples:**

Input:N = 12, K = 4Output:Yes

N = 1 + 2 + 4 + 5 = 12 (12 as sum of 4 distinct integers)

Input:N = 8, K = 4Output:No

**Approach:** Consider the series **1 + 2 + 3 + … + K** which has exactly **K** distinct integers with minimum possible sum i.e. **Sum = (K * (K – 1)) / 2**. Now, if **N < Sum** then it is not possible to represent **N** as the sum of **K** distinct positive integers but if **N â‰¥ Sum** then any integer say **X â‰¥ 0** can be added to **Sum** to generate the sum equal to **N** i.e. **1 + 2 + 3 + … + (K – 1) + (K + X)** ensuring that there are exactly **K** distinct positive integers.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <iostream>` `using` `namespace` `std;` `// Function that returns true if n` `// can be represented as the sum of` `// exactly k distinct positive integers` `bool` `solve(` `int` `n, ` `int` `k)` `{` ` ` `// If n can be represented as` ` ` `// 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(n >= (k * (k + 1)) / 2) {` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 12, k = 4;` ` ` `if` `(solve(n, k))` ` ` `cout << ` `"Yes"` `;` ` ` `else` ` ` `cout << ` `"No"` `;` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `import` `java.io.*;` `class` `GFG {` ` ` `// Function that returns true if n` ` ` `// can be represented as the sum of` ` ` `// exactly k distinct positive integers` ` ` `static` `boolean` `solve(` `int` `n, ` `int` `k)` ` ` `{` ` ` `// If n can be represented as` ` ` `// 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(n >= (k * (k + ` `1` `)) / ` `2` `) {` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `12` `, k = ` `4` `;` ` ` `if` `(solve(n, k))` ` ` `System.out.println(` `"Yes"` `);` ` ` `else` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `// This code is contributed by anuj_67..` |

## Python3

`# Python 3 implementation of the approach` `# Function that returns true if n` `# can be represented as the sum of` `# exactly k distinct positive integers` `def` `solve(n,k):` ` ` `# If n can be represented as` ` ` `# 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(n >` `=` `(k ` `*` `(k ` `+` `1` `)) ` `/` `/` `2` `):` ` ` `return` `True` ` ` `return` `False` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `n ` `=` `12` ` ` `k ` `=` `4` ` ` `if` `(solve(n, k)):` ` ` `print` `(` `"Yes"` `)` ` ` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by` `# Surendra_Gangwar` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG` `{` ` ` `// Function that returns true if n` ` ` `// can be represented as the sum of` ` ` `// exactly k distinct positive integers` ` ` `static` `bool` `solve(` `int` `n, ` `int` `k)` ` ` `{` ` ` `// If n can be represented as` ` ` `// 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(n >= (k * (k + 1)) / 2) {` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` `int` `n = 12, k = 4;` ` ` `if` `(solve(n, k))` ` ` `Console.WriteLine(` `"Yes"` `);` ` ` `else` ` ` `Console.WriteLine(` `"No"` `);` ` ` `}` `}` `// This code is contributed by ajit.` |

## PHP

`<?php` `// PHP implementation of the approach` `// Function that returns true if n` `// can be represented as the sum of` `// exactly k distinct positive integers` `function` `solve(` `$n` `, ` `$k` `)` `{` ` ` `// If n can be represented as` ` ` `// 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(` `$n` `>= (` `$k` `* (` `$k` `+ 1)) / 2) {` ` ` `return` `true;` ` ` `}` ` ` `return` `false;` `}` `// Driver code` `$n` `= 12;` `$k` `= 4;` `if` `(solve(` `$n` `, ` `$k` `))` ` ` `echo` `"Yes"` `;` `else` ` ` `echo` `"No"` `;` `// This code is contributed by ihritik` `?>` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function that returns true if n` `// can be represented as the sum of` `// exactly k distinct positive integers` `function` `solve(n, k)` `{` ` ` ` ` `// If n can be represented as` ` ` `// 1 + 2 + 3 + ... + (k - 1) + (k + x)` ` ` `if` `(n >= (k * (k + 1)) / 2)` ` ` `{` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` `}` `// Driver code` `var` `n = 12, k = 4;` `if` `(solve(n, k))` ` ` `document.write(` `"Yes"` `);` `else` ` ` `document.write(` `"No"` `);` `// This code is contributed by todaysgaurav` `</script>` |

**Output:**

Yes

**Time Complexity:** O(1)

**Auxiliary Space:** O(1)