Given two integers **N **and **K**, the task is to find the count of all possible **N-digit** numbers having sum of every **K** consecutive digits of the number are equal.**Examples:**

Input:N = 2, K=1Output:9Explanation:

All two digit numbers satisfying the required conditions are {11, 22, 33, 44, 55, 66, 77, 88, 99}

Input:N = 3, K = 2Output:90

**Naive and Sliding Window Approach:** Refer to Count of N digit Numbers whose sum of every K consecutive digits is equal for the simplest approach and Sliding Window technique based approach.**Logarithmic Approach:**

For the sum of **K**-consecutive elements to be always equal, the entire number is governed by its first **K** digits.

- The
**i**digit will be equal to the^{th}**(i-k)**digit for the number to satisfy the condition such that the sum of every^{th}**K**consecutive digit is the same.

Illustration:

N = 5 and K = 2

If the first two digits are 1 and 2, then the number has to be 12121 so that sum of every 2 consecutive digits is 3.

Observe that the first 2 digits i.e. the firstKdigits repeats itself.

Therefore, to solve the problem, the task is now to find out the total count of **K-digit** numbers which is equal to **10 ^{K }– 10^{(K-1)}**. Therefore, print the calculated value as the answer.

Below is the implementation of the above approach:

## C++

`// C++ Program to implement ` `// the above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to count the number of ` `// N-digit numbers such that sum of ` `// every K consecutive digits are equal ` `void` `count(` `int` `n, ` `int` `k) ` `{ ` ` ` `long` `count = (` `long` `)(` `pow` `(10, k) - ` `pow` `(10, k - 1)); ` ` ` ` ` `// Print the answer ` ` ` `cout << (count); ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 2, k = 1; ` ` ` `count(n, k); ` `} ` ` ` `// This code is contributed by Ritik Bansal` |

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## Java

`// Java Program to implement ` `// the above approach ` `class` `GFG { ` ` ` ` ` `// Function to count the number of ` ` ` `// N-digit numbers such that sum of ` ` ` `// every K consecutive digits are equal ` ` ` `public` `static` `void` `count(` `int` `n, ` `int` `k) ` ` ` `{ ` ` ` `long` `count ` ` ` `= (` `long` `)(Math.pow(` `10` `, k) ` ` ` `- Math.pow(` `10` `, k - ` `1` `)); ` ` ` ` ` `// Print the answer ` ` ` `System.out.print(count); ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `n = ` `2` `, k = ` `1` `; ` ` ` `count(n, k); ` ` ` `} ` `} ` |

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## Python3

`# Python3 program to implement ` `# the above approach ` ` ` `# Function to count the number of ` `# N-digit numbers such that sum of ` `# every K consecutive digits are equal ` `def` `count(n, k): ` ` ` ` ` `count ` `=` `(` `pow` `(` `10` `, k) ` `-` `pow` `(` `10` `, k ` `-` `1` `)); ` ` ` ` ` `# Print the answer ` ` ` `print` `(count); ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `n ` `=` `2` `; ` ` ` `k ` `=` `1` `; ` ` ` ` ` `count(n, k); ` ` ` `# This code is contributed by 29AjayKumar ` |

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## C#

`// C# Program to implement ` `// the above approach ` `using` `System; ` `class` `GFG{ ` ` ` ` ` `// Function to count the number of ` ` ` `// N-digit numbers such that sum of ` ` ` `// every K consecutive digits are equal ` ` ` `public` `static` `void` `count(` `int` `n, ` `int` `k) ` ` ` `{ ` ` ` `long` `count = (` `long` `)(Math.Pow(10, k) - ` ` ` `Math.Pow(10, k - 1)); ` ` ` ` ` `// Print the answer ` ` ` `Console.Write(count); ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `Main(String[] args) ` ` ` `{ ` ` ` `int` `n = 2, k = 1; ` ` ` `count(n, k); ` ` ` `} ` `} ` ` ` `// This code is contributed by Rohit_ranjan` |

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**Output:**

9

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

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