Generate an array with product of all subarrays of length exceeding one divisible by K Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Given two positive integers N and K, the task is to generate an array of length N such that the product of every subarray of length greater than 1 must be divisible by K and the maximum element of the array must be less than K. If no such array is possible, then print -1. Examples: Input: N = 3, K = 20Output: {15, 12, 5}Explanation: All subarrays of length greater than 1 are {15, 12}, {12, 5}, {15, 12, 5} and their corresponding products are 180, 60 and 900, which are all divisible by 20. Input: N = 4, K = 100Output: {90, 90, 90, 90} Approach: The given problem can be solved by the following observations: It can be observed that by making the product of every subarray of length 2 divisible by K, the product of every subarray of length greater than 2 will automatically be divisible by K. Therefore, the idea is to take two divisors of K, say d1 and d2, such that d1 * d2 = K and place them alternatively in the array. Follow the steps below to solve the problem: Initialize two integer variables d1 and d2.Check if K is prime. If found to be true, print -1.Otherwise, calculate the divisors of K and store two divisors in d1 and d2.After that, traverse from i = 0 to N - 1.Print d1 if i is even. Otherwise, print d2. Below is the implementation of the above approach: C++ // C++ program for the above approach #include <iostream> using namespace std; // Function to check if the required // array can be generated or not void array_divisbleby_k(int N, int K) { // To check if divisor exists bool flag = false; // To store divisors of K int d1, d2; // Check if K is prime or not for (int i = 2; i * i <= K; i++) { if (K % i == 0) { flag = true; d1 = i; d2 = K / i; break; } } // If array can be generated if (flag) { // Print d1 and d2 alternatively for (int i = 0; i < N; i++) { if (i % 2 == 1) { cout << d2 << " "; } else { cout << d1 << " "; } } } else { // No such array can be generated cout << -1; } } // Driver Code int main() { // Given N and K int N = 5, K = 21; // Function Call array_divisbleby_k(N, K); return 0; } Java // Java program for the above approach class GFG{ // Function to check if the required // array can be generated or not public static void array_divisbleby_k(int N, int K) { // To check if divisor exists boolean flag = false; // To store divisors of K int d1 = 0, d2 = 0; // Check if K is prime or not for(int i = 2; i * i <= K; i++) { if (K % i == 0) { flag = true; d1 = i; d2 = K / i; break; } } // If array can be generated if (flag) { // Print d1 and d2 alternatively for(int i = 0; i < N; i++) { if (i % 2 == 1) { System.out.print(d2 + " "); } else { System.out.print(d1 + " "); } } } else { // No such array can be generated System.out.print(-1); } } // Driver Code public static void main(String[] args) { // Given N and K int N = 5, K = 21; // Function Call array_divisbleby_k(N, K); } } // This code is contributed by divyesh072019 Python3 # Python3 program for the above approach # Function to check if the required # array can be generated or not def array_divisbleby_k(N, K): # To check if divisor exists flag = False # To store divisors of K d1, d2 = 0, 0 # Check if K is prime or not for i in range(2, int(K ** (1 / 2)) + 1): if (K % i == 0): flag = True d1 = i d2 = K // i break # If array can be generated if (flag): # Print d1 and d2 alternatively for i in range(N): if (i % 2 == 1): print(d2, end = " ") else: print(d1, end = " ") else: # No such array can be generated print(-1) # Driver Code if __name__ == "__main__": # Given N and K N = 5 K = 21 # Function Call array_divisbleby_k(N, K) # This code is contributed by AnkThon C# // C# program for the above approach using System; class GFG{ // Function to check if the required // array can be generated or not public static void array_divisbleby_k(int N, int K) { // To check if divisor exists bool flag = false; // To store divisors of K int d1 = 0, d2 = 0; // Check if K is prime or not for(int i = 2; i * i <= K; i++) { if (K % i == 0) { flag = true; d1 = i; d2 = K / i; break; } } // If array can be generated if (flag) { // Print d1 and d2 alternatively for(int i = 0; i < N; i++) { if (i % 2 == 1) { Console.Write(d2 + " "); } else { Console.Write(d1 + " "); } } } else { // No such array can be generated Console.Write(-1); } } // Driver Code public static void Main(string[] args) { // Given N and K int N = 5, K = 21; // Function Call array_divisbleby_k(N, K); } } // This code is contributed by AnkThon JavaScript <script> // Javascript program for the above approach // Function to check if the required // array can be generated or not function array_divisbleby_k(N, K) { // To check if divisor exists let flag = false; // To store divisors of K let d1 = 0, d2 = 0; // Check if K is prime or not for(let i = 2; i * i <= K; i++) { if (K % i == 0) { flag = true; d1 = i; d2 = K / i; break; } } // If array can be generated if (flag) { // Print d1 and d2 alternatively for(let i = 0; i < N; i++) { if (i % 2 == 1) { document.write(d2 + " "); } else { document.write(d1 + " "); } } } else { // No such array can be generated document.write(-1); } } // Given N and K let N = 5, K = 21; // Function Call array_divisbleby_k(N, K); // This code is contributed by suresh07. </script> Output: 3 7 3 7 3 Time complexity: O(N + ?K)Auxiliary space: O(1) Comment More infoAdvertise with us Next Article Analysis of Algorithms N nk14646 Follow Improve Article Tags : Misc Greedy Mathematical DSA Arrays divisibility subarray +3 More Practice Tags : ArraysGreedyMathematicalMisc Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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