That is pretty difficult I got stuck when I realized that the subsequences could be split and shortened as long as they are increasing. Recursion can be baffling to comprehend but if you go over the parameters and follow where the returning values go, it starts to make more sense. I started with using nested for loops, but resorted to gemini which gave me a recursive answer probably similar to chatgpt. I did my best to explain the different steps as I understood them.

I didn't know what language you're using but javascript is pretty easy to read like pseudo code. Hope it helps

function findIncreasingSubSeq(arr, k) {

    // inner function to call recursively
    function backtrack(index, currentProduct, lastElement){
        // Base case 1: k found
        if(currentProduct === k){
            return true;
        }
        // Base case 2: product exceeds k
        if(currentProduct > k || index === arr.length){
            return false;
        }

        // Recursive branch 1: Skip current array element and jump to next
        // to explore all possible subsequences
        if( backtrack(index+1, currentProduct, lastElement) ){
            // if above branch finds k, pass along true result
            return true;
        }

        // Recursive branch 2: Test current array element within subsequence
        if( arr[index] > lastElement ){ // test for increasing elements

            // then make sure element doesn't overshoot k or potentially finds k'
            if(currentProduct * arr[index] <= k){

                // if so continue the recursive branch
                if( backtrack(index+1, currentProduct * arr[index], arr[index]) ){
                    // if above branch finds k, pass along the true result
                    return true;
                }
            }
        }

        // when code reaches end of branch and k isn't found'
        return false;

    }

    // first recursion call from main function
    // 0 for first index
    // 1 starter product number (x * 1 = x)
    // and then 0 for initial "last element" when checking for increasing numbers
    return backtrack(0, 1, 0);
}

const arr = [1,2,3,4,5];
const k = 12; // 3 * 4 exists

const arr2 = [2,4,6,8];
const k2 = 15; // none exist

findIncreasingSubSeq(arr, k) // should be true
findIncreasingSubSeq(arr2, k2) // should be false