# Lexicographically Smallest Permutation of length N such that for exactly K indices, a[i] > a[i] + 1

Given two integers N and K, the task is to generate a permutation of N numbers (Every number from 1 to N occurs exactly once) such that the number of indices where a[i]>a[i+1] is exactly K. Print “Not possible” if no such permutation is possible.

Examples:

```Input: N = 5, K = 3
Output: 5 4 3 1 2
Starting 3 indices satisfying the condition
a[i] > a[i]+1

Input: N = 7, k = 4
Output: 7 6 5 4 1 2 3
```

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

Approach: Since the permutation should be lexicographically smallest with the condition satisfied for k indices i.e. a[i] > a[i+1]. So for that starting K+1 digits should be in decreasing order and remaining should be in increasing order. So just print the K numbers from N to 1. Then print numbers from 1 to N-K.

For example: N = 6, K = 4
Print K numbers from N to 1 i.e. 6, 5, 4, 3
Print N-K numbers from 1 to N-K i.e. 1, 2

Permutation will be 654312 i.e. Starting 4 indices satisfy a[i] > a[i+1] for i = 1 to k.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `void` `printPermutation(``int` `n, ``int` `k) ` `{ ` `    ``int` `i, mx = n; ` `    ``for` `(i = 1; i <= k; i++) ``// Decreasing part ` `    ``{ ` `        ``cout << mx << ``" "``; ` `        ``mx--; ` `    ``} ` `    ``for` `(i = 1; i <= mx; i++) ``// Increasing part ` `        ``cout << i << ``" "``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `N = 5, K = 3; ` ` `  `    ``if` `(K >= N - 1) ` `        ``cout << ``"Not Possible"``; ` ` `  `    ``else` `        ``printPermutation(N, K); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  ` `  `static` `void` `printPermutation(``int` `n, ``int` `k) ` `{ ` `    ``int` `i, mx = n; ` `    ``for` `(i = ``1``; i <= k; i++) ``// Decreasing part ` `    ``{ ` `        ``System.out.print( mx + ``" "``); ` `        ``mx--; ` `    ``} ` `    ``for` `(i = ``1``; i <= mx; i++) ``// Increasing part ` `        ``System.out.print( i + ``" "``); ` `} ` ` `  `// Driver Code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `            ``int` `N = ``5``, K = ``3``; ` ` `  `    ``if` `(K >= N - ``1``) ` `        ``System.out.print( ``"Not Possible"``); ` ` `  `    ``else` `        ``printPermutation(N, K); ` `    ``} ` `} ` ` `  `// This code is contributed by inder_verma.. `

## Python3

 `# Python3 implementation of the ` `# above approach  ` `def` `printPermutation(n, k):  ` ` `  `    ``mx ``=` `n  ` `    ``for` `i ``in` `range``(``1``, k ``+` `1``): ``# Decreasing part  ` `        ``print``(mx, end ``=` `" "``)  ` `        ``mx ``-``=` `1` `     `  `    ``for` `i ``in` `range``(``1``, mx ``+` `1``): ``# Increasing part  ` `        ``print``(i, end ``=` `" "``)  ` ` `  `# Driver Code  ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``N, K ``=` `5``, ``3` ` `  `    ``if` `K >``=` `N ``-` `1``:  ` `        ``print``(``"Not Possible"``)  ` ` `  `    ``else``: ` `        ``printPermutation(N, K)  ` ` `  `# This code is contributed ` `# by Rituraj Jain `

## C#

 `// C# implementation of the above approach ` `using` `System; ` `class` `GFG { ` ` `  ` `  `static` `void` `printPermutation(``int` `n, ``int` `k) ` `{ ` `    ``int` `i, mx = n; ` `    ``for` `(i = 1; i <= k; i++) ``// Decreasing part ` `    ``{ ` `        ``Console.Write( mx + ``" "``); ` `        ``mx--; ` `    ``} ` `    ``for` `(i = 1; i <= mx; i++) ``// Increasing part ` `        ``Console.Write( i + ``" "``); ` `} ` ` `  `// Driver Code ` ` `  `    ``public` `static` `void` `Main () { ` `            ``int` `N = 5, K = 3; ` ` `  `    ``if` `(K >= N - 1) ` `        ``Console.WriteLine( ``"Not Possible"``); ` ` `  `    ``else` `        ``printPermutation(N, K); ` `    ``} ` `} ` ` `  `// This code is contributed by inder_verma.. `

## PHP

 `= ``\$N` `- 1) ` `        ``echo` `"Not Possible"``; ` ` `  `    ``else` `        ``printPermutation(``\$N``, ``\$K``); ` ` `  ` `  `// This code is contributed by inder_verma.. ` `?> `

Output:

```5 4 3 1 2
```

Time Complexity: O(N)

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